Current Trends in Strongly Correlated and Frustrated Systems

I will discuss electronic correlations described by the Hubbard model from one to infinite dimensions (dynamical mean-field theory) and thereby connect with some of the research performed by Sriram over the last four decades.

Using the dynamical mean field theory we investigate the magnetic field dependence of dc conductivity in the Hubbard model on the square lattice, fully taking into account the orbital effects of the field introduced via the Peierls substitution. In addition to the conventional Shubnikov–de Haas quantum oscillations, associated with the coherent cyclotron motion of quasiparticles and the presence of a well-defined Fermi surface, we find an additional oscillatory component with a higher frequency that corresponds to the total area of the Brillouin zone. These paradigm-breaking oscillations appear at elevated temperature. This finding is in excellent qualitative agreement with the recent experiments on graphene superlattices. We elucidate the key roles of the off-diagonal elements of the current vertex and the incoherence of electronic states, and explain the trends with respect to temperature and doping. [1] Universal Magnetic Oscillations of dc Conductivity in the Incoherent Regime of Correlated Systems, Jakša Vučičević, Rok Žitko Phys. Rev. Lett 127, 196601 (2021) [2] Electrical conductivity in the Hubbard model: Orbital effects of magnetic field, Jakša Vučičević, Rok Žitko Phys. Rev. B 104, 205101 (2021)

In the context of interacting electron systems, topological invariants can be constructed by calculating the winding number of the map between the thermal Green’s function and its variables, the Matsubara frequency, the momentum, and, potentially, additional Hamiltonian parameters. Furthermore, it is believed that such invariants, constructed solely from the thermal Green’s function, coincide with physical invariants, such as the anomalous Hall conductance. However, there are examples where such one-to-one correspondence does not hold. For instance, there are model Mott insulators that possess a finite winding number without any observable topological property. In the talk, I provide a simple explanation of this discrepancy that yields rather unexpected implications. I demonstrate that the winding number purportedly representing the anomalous Hall conductance in two dimensions, as originally argued by Ishikawa and Matsuyama, in fact corresponds to the antisymmetric component of the conductivity tensor with the current vertices evaluated in the so-called static limit, i.e., the transferred frequency approaching zero faster that the transferred momentum. Conversely, the current vertices of the physical Hall conductance must be calculated in the opposite dynamic limit. Therefore, the two quantities may differ if and only if the two limits do not commute, which entails a non-analyticity at zero transferred frequency and momentum. This is only possible if there exist gapless excitations with their own “Fermi surface”. The immediate consequence is that the intrinsic anomalous Hall conductance of topological metals acquires Fermi liquid corrections, similar to other transport coefficients and thermodynamic susceptibilities. Consequently, the Berry curvature of the quasiparticle bands does not yield the correct value of the intrinsic anomalous Hall conductance. Furthermore, I explore the implications of our findings in the hypothetical scenario of a non-symmetry breaking doping-driven transition between a metal with finite intrinsic anomalous Hall conductance and the aforementioned model Mott insulator with a non-zero winding number but zero anomalous Hall conductance. I demonstrate that such a hypothetical transition is possible only if “neutral” quasiparticles, characterised by their own “Fermi surface”, emerge in the metal prior to the transition and persist in the Mott insulator.

The Mott problem stands as a grand challenge largely because its solution is at the heart of high-temperature superconductivity in the cuprates. It is unfortunate that such materials are largely 2-dimensional and the only exact solutions are restricted to d=1 with Bethe ansatz and infinite dimensions. I will present a method valid in any dimension that recovers the Bethe ansatz results in $d=1$ and the $d=\infty$ solutions as well. At the heart of the method is the breaking of an overlooked $Z_2$ symmetry of Fermi liquids . I will present benchmarks for the method in d=1 and compare with``accepted'' results in d=2, where no exact results are known. The same Z_2 symmetry breaking underlies the deviation of the Luttinger count from the physical charge.

I will talk about my work on the fixed-point structure of an interacting two-flavor fermionic system, applicable to Moiré systems near the valley polarization transition, where each flavor possesses a dispersion with a tunable real exponent "a". Starting from the Fermi liquid phase at weak interaction, we identify two possible Pomeranchuk/Stoner-type instabilities at stronger interaction. These instabilities lead to spontaneous spatial rotational or flavor symmetry breaking. Our key discovery is that one of these instabilities exhibits an RG fixed point that is attractive for "a<1", indicating a continuous transition. Conversely, for "a>1", the fixed point becomes repulsive, resulting in a discontinuous transition. We also investigate the collective modes driving these instabilities of Fermi liquids. This work predicts a universal Fermi surface deformation ratio at the continuous transition instability, which is experimentally observable.

Since Anderson's seminal proposal of a resonating valence bond (RVB) ground state in triangular Heisenberg magnets, geometric frustration has become a key paradigm in modern physics, driving the discovery of novel states of matter in quantum magnets. Its application to the exchange interactions governing the physics of Mott insulators has uncovered a wealth of emergent phenomena, which have been a central focus of this conference series. In a more recent seminal work, Jan Haerter and Sriram Shastry demonstrated that kinetic energy frustration gives rise to effective antiferromagnetic interactions in slightly doped triangular Mott insulators. I will argue that this result represents just the tip of an iceberg of emergent phenomena, encompassing polaron physics, unconventional pairing, and metallic RVB spin liquids exhibiting spin-charge separation—all driven by kinetic energy frustration. Moreover, we will explore how the metallic RVB liquid induced by this “counter-Nagaoka” effect emerges as an exact ground state in slightly doped Mott insulators on corner-sharing tetrahedral lattices.

Ideas about resonant valence bond liquid and spin-charge separation have led to key concepts in physics such as quantum spin liquids, emergent gauge symmetries, topological order, and fractionalisation. Despite extensive efforts to demonstrate the existence of a resonant valence bond phase in the Hubbard model that originally motivated the concept, a definitive realisation has yet to be achieved. Here, we present a solution to this long-standing problem by uncovering a resonant valence bond phase exhibiting spin-charge separation in realistic Hamiltonians. We show analytically that this ground state emerges in the dilute-doping and infinite-onsite-repulsion limit of a half-filled Mott insulator on corner-sharing tetrahedral lattices with frustrated hopping. We confirm numerically that the results extend to finite exchange interactions, finite-sized systems and finite dopant density. We further conducted a preliminary study on the nature of the excitations and spin-liquid correlations, suggestive of bosonic holon behaviour. Although much attention has been devoted to the emergence of unconventional states from geometrically frustrated interactions, our work demonstrates that kinetic energy frustration in doped Mott insulators may be essential for stabilising robust, topologically ordered states in real materials.

The Hubbard model, when combined with the ingredient of frustration, harbors kinetically induced magnetism, spin liquidity, and generalized Wigner crystallinity [1,2]. Many aspects of these theoretical findings are now being actively investigated in recently realized cold atom and solid-state (moiré) based emulators, which have reinitiated interest in the nature of magnetism and metallicity in various parameter regimes. Motivated by pioneering theoretical work of Nagaoka [Phys. Rev. 147, 392 (1966)] and Haerter-Shastry [Phys. Rev. Lett. 95,087202 (2005)], we revisit the role of kinetically frustrated magnetism, a phenomenon where magnetic order emerges without any underlying magnetic interactions, at finite hole density [3,4]. We numerically study the infinite-U triangular Hubbard model using the density matrix renormalization group (DMRG) algorithm and find that the kinetically induced 120-degree antiferromagnetic state remains stable up to a hole density of approximately 0.2. At higher concentrations of holes we report transitions to other phases including a renormalized metal, whose features we interpret analytically. We discuss the impact of our findings on the case of large but finite and realistic U, and investigate whether kinetic magnetism and superexchange collaborate or compete. [1] K. Lee, P. Sharma, O. Vafek, H. J. Changlani, Phys. Rev. B 107, 235105 (2023) [2] A. Kumar, C. Lewandowski, H. J. Changlani, arXiv: 2409.13814 (2024), under review [3] P. Sharma, H. J. Changlani, et al., in prep. [4] S. Sherif, P. Sharma, H.J. Changlani, in prep.

The Hubbard model at $U\to\infty$ has recently been shown to have resonant valence bond (RVB) ground states on the corner-sharing sawtooth and pyrochlore lattices in the dilute doping limit of a single vacancy. In an effort to further generalize those results, I study how the ground state is modified when not all corners are shared between two tetrahedra as in the quasi-1D lattices of a pyrochlore stripe, and how to approach the problem in the case of finite doping. Using a non-Abelian version of the flux inequality, the tetrahedron chain is shown to have degenerate RVB-like ground states. The Bethe ansatz (BA) is adapted to solve the sawtooth chain with spinless or spin-polarized fermions and multiple holons, which is the first example of applying BA to a quasi-1D lattice.

Strongly correlated systems such as high-Tc systems are experimentally very important and widespread in occurrence. Their analytical treatment using controlled methods is a highly challenging problem. It has been termed as one of the central problem in condensed matter physics. The usual methods using the interaction strength U as a perturbative parameter, are clearly undermined if U is very large. Sometimes U is even bigger than the band width. Thus procedures involving summation of classes of diagrams, etc. have dubious validity. This has created a large theoretical gap in the ``space of techniques''. The ECFL theory was launched in 2011, to bridge this gap. I review the basic ingredients of the ECFL theory- avoiding technical details as far as possible, and highlight the main outcomes of the recent efforts of our group, including a summary of the computation of resistivity in t-J model in 2-d, and compared with all available data on single layer Cuprate materials. I offer a perspective on what has been already been done within this theory, how it relates to theories like the Dynamical Mean Field Theory, and what remains to be done. I then discuss two predictions from the theory and its offshoots that are currently awaiting experimental verification. *) As an indirect offshoot of these studies we uncovered a method of inverting the spectral function to find the imaginary part of self energy of electrons from the angle resolved photoemission experimental data. When checked experimentally, these would reveal the fundamental characteristics of strongly correlated metals, namely whether they are Fermi liquids or not. *) Another offshoot of these studies is the development of photoemission sum-rules, which should reveal the fermi surface of underlying normal electrons, from data obtained purely in the superconducting state.

We will report our Laser ARPES studies on electron-mode coupling and persistent Fermi pocket formation in high temperature cuprate superconductors.

Moiré materials built on transition metal dichalcogenide semiconductors have emerged as a tunable platform for simulating the Hubbard model on a triangular lattice. A natural question arises: Can the platform be tuned to yield a phase diagram similar to that in high-temperature cuprate superconductors? In this talk, I will discuss the emergence of “high-temperature” superconductivity near the Mott transition in a triangular moiré lattice with intermediate coupling strength. The emergent doping-temperature phase diagram looks remarkably similar to that in cuprate superconductors. I will also discuss the evolution of the phase diagram by tuning the band structure of the material by gating. The results could provide a new angle for understanding the phenomenon of high-temperature superconductivity in strongly correlated materials.

Andreev spectroscopy is one of the few phase-sensitive experiments done on moire graphene superconductors (SC) that can shed light on the pairing symmetry. Its interpretation however is unclear, as STM experiments in the Andreev and tunneling regimes show two distinct energy scales whose origin is mysterious. We show using a Green’s function formulation that the two energy scales cannot be understood as a SC gap in the Andreev spectra and a pseudogap in tunneling. We also show that the ballistic Andreev regime can never be realized in moire SCs as the large mismatch in the Fermi velocity (vF) of the flat band SC and the STM tip renormalizes a transparent interface towards the tunneling regime. We discuss self-energy corrections to vF that determines the conductance. We model the Andreev experiment as a circular metallic disc embedded in an unconventional SC. With strong vF mismatch, the low bias conductance is dominated by tip-induced Andreev bound states which are responsible for the low energy scale distinct from the SC gap seen in tunneling.

The cuprate pseudogap phase displays Fermi arc spectral weight in photoemission, while recent magnetotransport observations present compelling evidence for hole pockets. We model the pseudgap by a Fractionalized Fermi liquid (FL*), which was predicted to have hole pockets of fractional area p/8 (where p is the doping), in agreement with the recently observed Yamaji angle. We employ a FL* state with a background critical spin liquid with an emergent SU(2) gauge field, similar to that found in the Shastry-Sutherland antiferromagnet; this describes Fermi arcs at intermediate temperatures. At lower temperatures, the fractionalized excitations are confined, and we obtain nodal d-wave superconductivity competing with a variety of charge-ordered states. I will also briefly mention the quantum criticality from FL* to the overdoped Fermi liquid, which yields a theory for the strange metal employing the two-dimensional Yukawa-SYK model.

In recent experimental work by the research group of Arindam Ghosh at IISc, unprecedented enhancements of electron-phonon interactions in systems of Ag nanoparticles dispersed in an Au matrix, seen via resistivity and point contact spectroscopy measurements, have been reported [Nature Communications 16, 61 (2025)]. In this talk I will present a theory we have developed [Phys. Rev. B 111. 184507 (2025)] that explains these observations. The theory is based on a simplified semi-phenomenological tight-binding model with Coulomb interactions included as regards the electrons in these systems; and a simplified semi-phenomenological force constant model for the phonons. The mechanism responsible is the formation of (nearly) dipolar charge redistributions at the Au-Ag interfaces, and their strong coupling, via Coulomb interactions, with the breathing and other modes of vibration of the lighter Ag atoms caged inside the heavier Au matrix. The interface dipoles form because of the interplay between the mismatch of the local potential seen by the electrons at the Ag and Au sites and the (long-range) Coulomb repulsion between electrons. I will also discuss the implications of this mechanism for obtaining high-$T_c$ superconductivity in such systems.

Non-equilibrium control of electronic properties in condensed matter systems can result in novel phenomenon. In this talk, I will discuss our recent works in which we provide a non-equilibrium route to realize a half-metal as well as unconventional superconductivity. Basically we explore the periodically driven weakly interacting Hubbard model. The drive induces staggered second and third order hopping and a staggered potential between two sublattices. Close to the dynamical freezing point, due to suppression of nearest neighbour hopping in the driven system, an effective enhancement of various terms in the Floquet Hamiltonian including the e-e occurs. Depending the drive parameters the driven system may have intermediate strength of interactions for which half-metallic phase is realized while if the driven system has extremely strong e-e interactions, spin-exchange mediated superconductivity can be realized even when the overall system is at half-filling. These phases achieved at high drive frequency and high drive amplitude should be stable for exponentially large time scale in the drive frequency and amplitude and can have potential applications in spintronics and other upcoming quantum technologies.

The observed robust quantized Hall conductances in quantum Hall systems and Chern insulators have so far been understood in terms of the topology of isolated systems. Namely those which are not coupled to the leads. However, it is not clear if these topological arguments extend to systems which are coupled to leads. Namely, is the quantization independent of the parameters of the leads and its coupling to the sample? We address this question, within a model of a Chern insulator with a cylindrical geometry. We show that for a model of the leads which consist of a set of $1-d$ decoupled wires, the Hall conductance can be identified with a topological invariant expressed in terms of the scattering states. We also give an example of a model of the leads where the Hall conductance is not quantized.

Motivated by recent discovery of three sets of topologically non-trivial phases of matter in lattice models beyond established classification schemes, we generalise the framework of the quantum Hall effect (QHE) to that of the quantum skyrmion Hall effect (QSkHE). The essential generalisation of the QSkHE is that a single quantum spin of S small (e.g., 1/2, 1, 3/2, etc.), and multiplicity 2S+1, is more accurately treated in some cases as realizing an almost point-like---yet intrinsically 2+1-dimensional (2+1 D)---quantum Hall droplet formulated in terms of a generalisation of matrix gauge theory of Susskind and Polychronakos. This quantum Hall droplet also possesses a holographic description in terms of Calogero models, one-dimensional harmonic oscillators with fractional exclusion statistics. The consequences are that a single spin can exhibit fractional statistics, quasi-hole/particle charged excitations (which we collectively refer to as quantum skyrmions), and incompressibility with measurable consequences for individual spins as well as extended systems of multiple spins. For a 2D array of spins, each realising a point-like 2+1 D quantum Hall droplet, the intrinsic dimensionality of the topological state realised by the entire system is up to 2+2+1 D. That is, the treatment of spin for S small as an internal degree of freedom (DOF) or isospin, and effectively just a label of quantum states, is an approximation that can fail. The quantum skyrmions can play the role, in the QSkHE, that charged particles play in the QHE.

It has been realized over the past two decades that topological nontriviality can be present not only in insulators but also in gapless semimetals, the most prominent example being Weyl semimetals in three dimensions. Key to the topological classification schemes are the three ``internal" symmetries, time reversal ${\cal T}$, charge conjugation ${\cal C}$, and their product, called chiral symmetry ${\cal S}={\cal T}{\cal C}$. In this work, through explicit calculations, we show that robust topological semimetal phases occur in $d=3$ without invoking crystalline symmetries other than translations. These semimetals appear not only as intermediate gapless phases between the topological and the trivial insulators in symmetry classes that have nontrivial topology, but also in symmetry classes that have only trivial insulators in $d=3$. We show that all classes that do not have chiral symmetry always have topologically stable and robust phases with Weyl nodes, classified by their Chern number on an enclosing surface. Furthermore, all classes that have chiral symmetry always have topologically protected and robust nodal line semimetal phases, classified by the winding number of a linking loop. Just as point nodes imply Fermi arcs on the surface Brillouin zone (BZ), a nonzero winding number on a nodal loop implies robust gapless drumhead states on the surface BZ.

Most existing quantum Hall interferometers measure twice the braiding phase, $e^{i2\theta}$, of Abelian anyons, i.e.~the phase accrued when one quasi-particle encircles another clockwise. I will describe our theoretical proposal for a modified Fabry--P\'{e}rot or Mach--Zehnder interferometer that can measure $e^{i\theta}$.

I discuss the emergence of the Hubbard model with imaginary hopping in open quantum systems described by certain Lindblad equations. More generally, I show that solutions to the "decorated Yang-Baxter equation" introduced by Shastry give rise to integrable Lindblad equations. The BBGKY hierarchy arising from the Lindblad equation decouples level-by-level, which makes it possible to obtain exact hydrodynamic projections of Heisenberg-picture operators, and determine linear-response functions in Lindbladian pump-probe settings.

Experiments with nearly-integrable ultracold one-dimensional quantum gases have probed integrability preserving dynamics involving large distances and long times, testing the recently proposed theory of generalized hydrodynamics. Using "high-energy" quenches implemented via a Bragg scattering pulse, the experiments have also unveiled fast local equilibration at the shortest available time scales, a process known as hydrodynamization in the context of relativistic heavy-ion collisions. I will discuss the experimental results and their theoretical understanding and modeling. For hydrodynamization, I will argue that integrability provides a theoretical framework from which one can draw a general picture that is expected to apply to nonintegrable systems.

I will begin with a review of integrable matrix theory—an analogue of random matrix theory for integrable systems—showing how level statistics, exact solvability, and level crossings emerge from the presence of nontrivial integrals of motion alone. Typical integrable matrices exhibit Poisson level statistics when the number of conserved quantities grows at least logarithmically with the Hilbert space dimension; otherwise, they show level repulsion. Exceptions to the Poisson statistics occur at isolated coupling values or when correlations are introduced between typically independent parameters. In the second part, I turn to time-dependent integrability and present exact solutions of non-stationary Schrödinger equations for the BCS and Kondo models with time-dependent couplings. I will show that the mean-field description of nonequilibrium superconductivity becomes exact in the thermodynamic limit for local observables but fails for global quantities such as the entanglement entropy and Loschmidt echo. The analysis reveals that time-dependent models based on the classical Yang–Baxter structure map to Knizhnik–Zamolodchikov equations, while those rooted in quantum Yang–Baxter algebra correspond to quantum Knizhnik–Zamolodchikov equations.

Wigner crystals are predicted to form in a very dilute and clean two-dimensional electron system when Coulombic repulsion dominates the kinetic energy, causing the electrons to freeze into a lattice. In this talk, we present transport signatures of electron- and hole-like Wigner solids in thin films of cadmium arsenide (Cd3As2) with thicknesses near the topological transition. Switching current-voltage (I-V) behavior is observed as the pinned solid is freed from the disorder potential by a finite bias. Hysteresis and voltage fluctuations in the I-V appear due to domain motion, which disappear simultaneously when the solid is depinned. Furthermore, the transport signatures disappear above a critical temperature as thermal fluctuations overcome the pinning potential. These Wigner solids are present at zero magnetic field and, surprisingly, are destroyed by a small field, in contrast to previous reports of Wigner solids in 2DEGs. We discuss their unconventional origin involving spatial inversion asymmetry and spin-orbit coupling.

Quantum Spin Ice is a U(1) spin liquid which is known to possess an emergent Quantum Electrodynamics and elementary excitations which correspond to gapped electric and magnetic monopoles as well as gapless emergent photons. The search for real materials that are candidates for such a quantum disordered ground state has recently focussed on Ce-based pyrochlore insulators, such as Ce$_2$Zr$_2$O$_7$, Ce$_2$Sn$_2$O$_7$ and Ce$_2$Hf$_2$O$_7$. The Ce$^{3+}$ ion in this environment possesses a pseudo spin 1/2 degree of freedom which originates from its CEF Kramer's doublet. The wave function for this doublet corresponds to Jz=+/- 3/2, which then gives pseudo spin S$^z$ a dipole magnetic moment, but pseudo spin 1/2 S$^x$ and S$^y$ carry octupolar moments. Hence these materials are referred to as dipole-octuple pyrochlores. Theoretical work based on a symmetry-allowed XYZ Hamiltonian predicts ground states that are both ordered and quantum disordered spin ices, each of which can be dominated by either the pseudo spin's dipolar or octupolar components. We and others have been actively characterizing the three Ce-based pyrochlores discussed above, by a variety of techniques including neutron scattering and low temperature thermodynamics. I will review these efforts, as well as the current status of the nature of their ground states

Multipolar magnets feature ordering and fluctuations of non-dipolar degrees of freedom such as quadrupoles, octupoles, etc. We explore how Einstein phonons can couple to and impact the dynamics of such multipolar magnets. We show that pumped or driven phonons can reveal the presence of "hidden order" in a manner similar to how pulsed fields can probe precessional spin dynamics in NMR. We also show the converse effect, namely the imprint of multipolar magnetism in the phonon spectrum, specifically how octupolar order can lead to pseudochiral phonons, which extends the recent ideas on how dipolar order imprints itself into chiral phonon modes.

The pyrochlore magnet has long been a fertile ground for the exploration of quantum and classical spin liquids, as well as other exotic magnetic phases, owing to its strong geometric frustration. Recently, the discovery of dipolar-octupolar pyrochlore materials has generated considerable interest in this field. Thermodynamic and neutron scattering experiments have identified promising candidates for dipolar-octupolar quantum spin ice, while theoretical studies have advanced our understanding of their phase diagrams and experimental signatures. In this talk, I will present recent progress on both classical and quantum dipolar-octupolar pyrochlore spin systems subjected to external magnetic fields. The presence of octupolar symmetry leads to qualitatively new behavior beyond that of conventional dipolar models. Our findings include classical spin fragmentation, novel quantum spin liquid phases, and tunable emergent photon dynamics. These results provide timely guidance for interpreting and designing near-future experiments on dipolar-octupolar pyrochlore compounds.

This talk is dedicated to the short-range magnetic order, energy scales, and the possibility of quantum spin liquids (QSLs) in geometrically frustrated magnets (GFMs), the largest class of materials in which QSLs are sought. I will present analyses of experimental data on spin-glass phase transitions, neutron-scattering intensity, and heat capacity in GFMs, which demonstrate the existence of a characteristic temperature, which we call the “hidden energy scale” and below which the cleanest available GFM undergo a transition to a spin-glass state incompatible with a QSL. I will present scenarios of the hidden energy scale and analyze its interplay with quenched disorder. I will demonstrate that the presence of vacancy defects, the most common type of quenched disorder, leads to a characteristic low-temperature anomaly, similar to the Schottky anomaly, in the specific heat of GFMs and also result in the increase of the magnetic susceptibility of the system. The hidden energy itself, however, comes from a crossover in the properties of clean GF materials, at which the material develops characteristic short-range order and, in the presence of sufficient quenched disorder, spin-glass freezing.

Quantum spin ice is a prototypical system exhibiting a quantum spin liqud phase, where the ground state is a macroscopic superposition of nontrivial magnetic textures described by 2-in 2-out ice rule [1]. Quantum spin ice hosts two species of fractional excitations, called electric and magnetic monopoles. Due to the coupling to background gauge fields, these fractional excitations are endowed with several unusual features absent in conventional quasiparticle. In this talk, we model the quantum spin ice with spin-1/2 quantum XXZ model defined on a pyrochlore lattice and address the dynamics of monopole excitations. We show that the interaction with gauge field introduces a strong spectral-edge singularity in the dynamics of magnetic monopole [2], which can be associated with the recent inelastic neutron scattering experiment on Ce2Sn2O7 [3]. We further address the spectrum of dual electric monopole, which is obtained by the combination of quantum Monte Carlo simulation and the stochastic analytical continuation techniques [4]. We determine the mass gap and the effective interaction of electric monopole and discuss how they can be observable in realistic experiments. [1] “Spin ice” (Springer International Publishing, 2021), ed. by M. Udagawa and L. D. C. Jaubert. [2] M. Udagawa and R. Moessner, Phys. Rev. Lett. 122, 117201 (2019). [3] V. Pore ́e et al., Nat. Phys. 21, 83-88 (2025). [4] J. M. Cruz, H. Suwa and M. Udagawa, in preparation.

We identify the many-body counterpart of flat bands, which we call many-body caging, as a general mechanism for non-equilibrium phenomena such as a novel type of glassy eigenspectrum order and many-body Rabi oscillations in the time domain. We focus on constrained systems of great current interest in the context of Rydberg atoms and synthetic or emergent gauge theories. We find that their state graphs host motifs which produce flat bands in the many-body spectrum at a particular set of energies. Basis states in Fock space exhibit Edwards-Anderson type parameters in the absence of quenched disorder, with an intricate, possibly fractal, distribution over Fock space which is reflected in a distinctive structure of a non-vanishing post-quench long-time Loschmidt echo, an experimentally accessible quantity. In general, phenomena familiar from single-particle flat bands manifest themselves in characteristic many-body incarnations, such as a reentrant `Anderson' delocalisation, offering a rich ensemble of experimental signatures in the abovementioned quantum simulators. The variety of single-particle flat band types suggests an analogous typology--and concomitant phenomenological richness to be explored--of their many-body counterparts.

The Shastry-Sutherland lattice, also known as the orthogonal dimer lattice, is a paradigmatic geometry of frustrated magnetism both for classical and quantum spins. In this talk, I will report on extensive tensor network simulations of that model that have allowed us to understand the remarkably rich phase diagram of the spin-1/2 Shastry-Sutherland SrCu$_2$(BO$_3$)$_2$ under pressure and magnetic field, and the intriguing magnetization plateaus of Er$_2$Be$_2$GeO$_7$, a recent rare-earth based realization of the Ising model on the Shastry-Sutherland lattice.

Neutron spectroscopy offer a unique insight into the emergent quantum phases and entangled dynamics in quantum materials. A textbook example is offered by the compound SrCu$_2$(BO$_3$)$_2$ realizing the Shastry-Sutherland model, which reveal a plethora of intriguing phenomena including: bosonic flat bands; a zoo of entangled bound states; correlated decay of magnons; valence bond solid of plaquette singlets; a quantum equivalent to the critical point of water; a putative deconfined quantum critical point; fractional magnetization plateaus and bosonic BEC of triplet bound states. Exploring this rich physics illustrates the challenges and rewards of technological advancements in neutron instrumentation and pushing the capabilities of extreme condition sample environments. [1] M. Zayed et al, Phys Rev Lett (2014) [2] M. Zayed et al, PNAS (2017) [3] J Larrea et al, Nature (2021) [4] E. Fogh et al, Nat Com (2024) [5] E. Fogh et al, Phys. Rev. Lett. 133, 246702 (2024) [6] E. Fogh et al, Rev Sci Inst. 96, 043902 (2025)

Building upon the seminal work by Shastry and Sutherland in 1981 I report on our findings of a theorem for exact quantum antiferromagnets on 2D lattices. We find the maple leaf lattice to be a preeminently suited domain for a Shastry Sutherland-type phenomenological setup, and summarise the current understanding of our maple leaf model.

We present a multimethod investigation into the nature of the recently reported quantum spin liquid (QSL) phase in the spin-$1/2$ Heisenberg antiferromagnet on the Shastry-Sutherland lattice with superexchange coupling $J_s$ ($J_d$) on the square (dimer) bonds. A comprehensive projective symmetry group classification of fermionic mean-field \textit{Ans\"atze} on this lattice yields 46 U(1) and 80 $\mathbb{Z}_{2}$ states. Our density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations assessing the fidelity and level spectroscopy suggest that the Shastry-Sutherland, the square-lattice and checkerboard lattice $J_{1}$-$J_{2}$ Heisenberg antiferromagnets share the same QSL phase. This motivates us to establish a mapping of our \textit{Ans\""atze} to those of the square lattice and identify the equivalent of the square-lattice $\mathbb{Z}_{2}$ Dirac QSL (Z2A$zz$13) in the Shastry-Sutherland and checkerboard systems. Employing state-of-the-art variational Monte Carlo calculations with Gutzwiller-projected wavefunctions improved upon by Lanczos steps, we demonstrate the excellent agreement of energies and correlators between a gapless (Dirac) $\mathbb{Z}_{2}$ spin liquid---characterized by only few parameters---and approaches based on neural quantum states and DMRG. Furthermore, the decay of the real-space spin-spin correlations is shown to evolve from $\sim 1.3$ (in the Shastry-Sutherland limit) to $\sim 1.8$ (for the square lattice $J_{1}$-$J_{2}$) as we traverse the QSL region connecting the two models. We apply the recently developed Keldysh formulation of the pseudo-fermion functional renormalization group to compute the dynamical spin structure factor

to be sent

Quantum spin systems have remarkable properties, ranging from magnetic order to various forms of spin liquids. This physics is particularly spectacular in low dimension such as for quantum chains and ladders, where the excitations in such systems are exotic: spinons instead of magnons or gapped systems. I will discuss in this talk several examples of such systems both from the theoretical point of view but also in connection with experiments in NMR and neutrons. I will also show that such systems can be used as efficient quantum simulators, in the same spirit than cold atomic gases have been very successfully used in connection with correlated quantum systems.

Quantum spin liquids (QSLs) are long-range entangled states of matter of billions of interacting qubits or spins that develop in a Mott insulator. Remarkably QSLs harbor fractionalized excitations rather than the conventional spin waves of ordered magnets that carry integer units of angular momentum. In my talk I will identify detectable signatures of these fractionalized excitations in pump-probe spectroscopy. These fractionalized excitations are promising candidates to create logical qubits for quantum computation.

We discuss lattice $S=\frac{1}{2}$ quantum Hamiltonians with bond-dependent Ising couplings with a mutually anticommuting algebra of extensively many local $Z_2$ conserved charges. This mutual algebra is like the algebra of quantum spin-$\frac{1}{2}$ local degrees of freedom however arising in the structure of the local conserved charges. As provable consequences, these models have finite residual entropy density in the ground state with a simple but non-trivial degeneracy counting and concomitant quantum spin liquidity. The spin liquidity relies also on a geometrically site-sharing property of the local conserved $Z_2$ charges. This can be contrasted to for example the bond-sharing property of the local conserved $Z_2$ charges on the hexagonal plaquettes of the Kitaev honeycomb spin-$\frac{1}{2}$ model which leads to a mutually commuting algebra. We will discuss the many-body order that can be present within the class of anticommuting quantum spin liquids co-existing with extensive residual ground state entropy. We will also discuss the connections and differences of this kind of quantum spin liquidity in relation to the many-body topological order found in some gapped quantum spin liquids whose canonical example is the Kitaev toric code.

The ground-state phase diagram of the Heisenberg model on a triangular lattice, which includes both nearest-neighbor ($J_1$) and next-nearest-neighbor ($J_2$) super-exchange couplings, hosts a variety of different phases. We use simple Gutzwiller-projected fermion wave functions to describe these phases, including those that emerge when an external magnetic field is applied. We pay particular attention to the gapless and gapped states that appear at finite magnetization values in the highly-frustrated regime of $J_2/J_1=1/8$.

We present new results on the phase diagram of the $J_1-J_2$ triangular lattice antiferromagnet in a magnetic field. Focusing on the putative quantum spin liquid regime of $J_2/J_1 ~ 0.1$, we find the appearance of two magnetization plateaus, at 1/3 and 1/2 of the total magnetization, in the magnetic field. We also discuss the dynamical response of the model and the evolution of the Dirac spin liquid with the magnetic field.

For quantum spin systems in equilibrium, the dynamic structure factor (DSF) is among the most feature-packed experimental observables. However, from a theory perspective it is often hard to simulate in an unbiased and accurate way, especially for frustrated and high-dimensional models at intermediate temperature. We address this challenge by introducing a dynamic extension of the high-temperature expansion as an efficient numerical approach to the DSF for arbitrary lattices. We focus on Heisenberg and XXZ models and spin-lengths S=1/2 and 1. For the latter, we also target the quadrupolar correlations. We present a user-friendly numerical implementation and provide comprehensive benchmarks on spin chains. As applications we treat a variety of frustrated two- and three dimensional antiferromagnets. In particular we shed new light on the anomalous intermediate temperature regime of the S=1/2 triangular lattice model and reproduce the DSF measured recently for a S=1 pyrochlore material.

Chirality is a source of novel phenomena and functionalities in biology, medicine, chemistry, elementary particle physics as well as condensed matter physics. Study of chiral magnets serves as one of the routes to find new functionality through new states of matters involving skyrmions and chiral solitons. In contrast to existing theoretical studies, most of which were carried out within a semiclassical framework, we developed a purely quantum mechanical theory for chiral magnetic chain. We find that magnetization process behaves in a markedly different way depending on whether the spin quantum number is half-odd integer (S=1/2, 3/2) or integer (S=1, 2). This work* has been done in collaboration with Sohei Kodama(U-Tokyo, Komaba) and Akihiro Tanaka (NIMS). Sohei Kodama, Akihiro Tanaka, and Yusuke Kato "Spin parity effects in monoaxial chiral ferromagnetic chain" Phys. Rev. B 107, 024403 (2023)

Frustrated magnets provide fertile ground for unconventional orders and emergent excitations. In particular, chiral states break time-reversal symmetry and host emergent gauge fluxes that can endow quasiparticles with nontrivial topology. Here, we explore two complementary aspects: topological magnon transport and exactly solvable spin models. On the triangular lattice, we study a spin-1/2 isotropic Heisenberg model with further-neighbor exchanges and ring exchange. The four-site ring exchange stabilizes a chiral four-sublattice noncoplanar order, which generates finite Berry curvature in the magnon bands and produces a thermal Hall effect even without Dzyaloshinskii-Moriya interactions. Using variational methods, we further show that this ordered phase can melt into a chiral spin liquid, continuously connected to the $U(1)$ Dirac spin liquid in the absence of ring exchange. In parallel, we construct a class of SU(2)-symmetric spin-S Hamiltonians whose ground states form an extensively degenerate manifold of chiral product wave functions. These exact ground states arise from spin-coherent states obeying a four-coloring rule on tetrahedral units. The construction naturally generalizes to a broad family of four-site Hamiltonians, applicable to lattices of corner- or edge-sharing tetrahedra such as the pyrochlore and the fcc lattices, to the honeycomb lattice with first- and second-neighbor interactions built from distorted tetrahedra, and even to the triangular lattice mentioned above. This framework provides a versatile platform for exploring chiral and multipolar orders across both two- and three-dimensional frustrated magnets.