Fluctuations, Quenched Disorder, and Strong Correlations

Moiré transition-metal dichalcogenide (TMD) bilayers have emerged as highly tunable platforms for realizing strongly correlated and topological quantum phases. In this work, we discuss how strong electronic correlations, long range interactions and band structure singularities cooperate to stabilize unconventional and topological superconductivity in TMD moiré systems. Using effective single-band descriptions of moiré flat bands treated within the Gutzwiller approximation, I first show that unconventional superconductivity in TMD bilayers can remain robust even in the presence of substantial intersite Coulomb repulsion. In the strongly correlated regime near half filling, renormalization effects suppress the detrimental impact of long range interactions, leading to a two-dome superconducting structure separated by a Mott insulating phase. This mechanism is particularly relevant for WS2/WSe2 heterobilayers. We demonstrate that spin-orbit induced interactions can drive topological superconductivity with mixed singlet–triplet pairing in twisted WSe2 bilayers. The resulting phase diagram hosts superconducting states characterized by nonzero Chern numbers, with experimentally controllable parameters enabling topological phase transitions. Finally, We show that optimal superconductivity can emerge when a Van Hove singularity is tuned to half-filling via a displacement field. The enhanced density of states, combined with correlation-induced renormalization, stabilizes pairing only within a narrow region of the phase diagram, consistent with recent experimental observations. These results highlight moiré TMDs as versatile systems for engineering correlated and topological superconducting phases.

We considered the phonons in monolayer graphene and we show the possibility for the spin-triplet superconducting excitations states by discretizing the single-particle excitations near the Fermi wave vector. The monolayer graphene was supposed to be exposed under the influence of the external gate-potential and the local Coulomb interaction effects have been taken into account at each lattice site position in the monolayer graphene. A sufficiently large domain of temperature was found, where the spin-triplet superconducting order parameter is not vanishing. Corresponding to this, at the surprisingly high temperature limit, we obtain a narrow domain of the effective electron-phonon interaction parameter, emphasizing the superconducting state. We discuss the localizing role of Hubbard-U interaction, the effects of the external gate potential, and the effect of doping on the calculated physical parameters in the system. We explain the importance of the chemical potential in the formation of the superconducting state. We show the existence of a large superconducting band-gap in the system even in the case of the absence of the applied electric field potential.

Dynamical heterogeneity, fractality, and topology are central concepts in modern condensed matter physics. Their origin is typically rooted in very different physical settings and microscopic mechanisms, such as glassy dynamics, quenched disorder and the absence of symmetry breaking. We show here that a simple, clean lattice model -- in thermal equilibrium -- hosts all three simultaneously. The dynamical heterogeneity even persists across a thermal phase transition into a long-range ordered nematic phase. Investigating the dynamics of the ordered phase, we find that the motion of its fractionalized quasiparticles is restricted to an emergent fractal network, leading to subdiffusive yet ergodic transport that deviates from conventional hydrodynamic expectations. The fractal exhibits critical scaling from the lattice scale up to long-wavelengths. This fractal structure also shapes the distribution of quasiparticle lifetimes, enhancing short-time dynamics. We discuss how this subdiffusive behavior can be probed experimentally in candidate materials through the power spectral density of the magnetization. Indeed, our results account for recent experimental results on dynamical heterogeneity in the spin ice compound $\mathrm{Dy_2Ti_2O_7}$ [arXiv:2408.00460] by identifying generation recombination noise of its fractionalized quasiparticles as the cause of dynamical heterogeneity. Our results show that dynamical heterogeneity can act as a diagnostic of new cooperative regimes, helping to transcend naive boundaries between equilibrium and non-equilibrium physics and between order and disorder.

Motivated by recent observations of fractional Chern insulators (FCIs) in the vicinity of superconducting (SC) phases (e.g. $\text{MoTe}_2$), we study fractional quantum (anomalous) Hall-superconductor heterostructures in the presence of U(1) order-parameter fluctuations and particularly focus on the case of $\nu=2/3$ quantum Hall states leading to $Z_3$ parafermions. While the emergence of $Z_3$ parafermions has already been demonstrated in the spin-unpolarized Halperin State, we demonstrate how disorder can also stabilize $ Z_3$ parafermions in the spin-polarized $nu=2/3$ state, which is expected to be present in $\text{MoTe}_2$. Due to a broad phase transition between the FCI and the superconducting state, we further study the effect of phase fluctuations on the $Z_3$ parafermions, using field-theoretical methods as well as the density-matrix renormalization group. We find a rich phase diagram composed of Mott insulating phases and two distinct Luttinger liquids, whose fundamental excitations carry charges 2e and 2e/3, respectively. In agreement with analytical considerations using conformal field theory, we numerically find transitions of Berezinskii-Kosterlitz-Thouless (BKT) type as well as a continuous $Z_3\times\text{U(1)}$ second-order phase transition characterized by central charge c = 9/5.

Strongly correlated materials are characterized by the competition of multiple energy scales, often leading to exotic phases of matter, with unique fingerprints. Among them are frustrated magnets, which often present long-range entanglement and fractionalized excitations, and Kondo systems, which host exotic heavy-liquid phases and unconventional superconductivity. Several of these phases are difficult to obtain experimentally in equilibrium. Floquet engineering allows for an external way of driving and stabilizing phases in materials using periodic fields, such as monochromatic light. We consider the Floquet engineering of ruthenate and iridate Hubbard models, as well as a magic-angle twisted bilayer graphene (MATBG) heavy-fermion model. In frustrated magnets, we induce frustration by using circularly polarized light to enhance the Kitaev interaction and suppress the Heisenberg interaction, to melt the magnetic order observed in equilibrium conditions. In MATBG, we also use circular light to induce Kondo channels that did not exist in equilibrium, allowing competition between them to obtain an effective two-channel Kondo lattice.

We investigate the effects of disorder and dissipation on the nematic phase transition of the J1-J2 model. Random interactions generate both random-mass and random-field terms that couple to the nematic order parameter. In the J1 < 2J2 regime, the nematic physics can be mapped onto an effective Hamiltonian resembling a random transverse-field Ising model with additional random longitudinal fields. Dissipation is incorporated by coupling each effective Ising variable to its own bath of harmonic oscillators. We aim to extend the strong-disorder renormalization group (SDRG) method to analyze this effective model.

Finite-momentum pairing, exemplified by Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, represents a paradigmatic form of unconventional superfluidity driven by Fermi-surface mismatch. Despite long-standing theoretical and experimental interest, its detection in two-dimensional systems has remained elusive. Here we study a doped, spin-imbalanced attractive Hubbard model using a combined computational and experimental approach. Experimentally, the model is realized with an ultracold atomic gas in an optical lattice and probed by quantum gas microscopy, while computationally it is studied using state-of-the-art constrained-path (CP) auxiliary-field quantum Monte Carlo (AFQMC). Direct comparisons between experiment and computation show quantitative agreement for various short-range magnetic and charge correlations at all temperatures accessed by experiment. We then investigate these correlations, together with pairing correlation functions, at lower temperatures using CP-AFQMC. Broad regimes in density and magnetization are found with signatures of FFLO order. We determine systematically the temperature-dependent properties and identify spin–XY correlations as a proxy signal closely associated with FFLO physics that is directly accessible by experiment.

The bilayer nickelate La$_3$Ni$_2$O$_7$ has recently been discovered to exhibit high-temperature superconductivity in bulk samples under pressure and in compressively strained thin films. At the same time, its normal state displays spin stripe order with wavevector $Q=(\pi/2,\pi/2)$ under ambient conditions. In this talk, we report results on superconductivity and magnetism arising from the interplay between Hund’s coupling $J_H$ and interlayer superexchange $J_z$ as the key interactions. We propose a microscopic Hamiltonian that captures the structural evolution from the orthorhombic to the nearly tetragonal regime under pressure, and use DMRG to show that the $(\pi/2, \pi/2)$ spin stripe order emerges in our model at sizable $J_H$ from a hidden quasi-one dimensionality. Upon increasing $J_z$, our model develops superconductivity in the crossover between Hund’s-coupling-dominated and interlayer-superexchange-dominated regimes. Complementary RPA calculations for a tight binding model fitted to recent ARPES measurements reveal competing $s_\pm$- and $d$-wave pairing tendencies, with Hund’s coupling tuning between the two. Together, these results highlight the key role played by Hund’s coupling in determining the nature of superconductivity and magnetism in this system.

We investigate quench dynamics in the quantum $S=1/2$ XXZ antiferromagnetic chain with staggered and anisotropic interactions in the flat-band limit. Our quench protocol interchanges the odd- and even-bond strengths of a fully dimerized chain, enabling us to derive exact time-dependent states for arbitrary even system sizes by working in the Bell basis. We obtain closed-form, size-independent expressions for the von Neumann and second-order R\'enyi entanglement entropies. We further calculate exact Loschmidt echoes and the corresponding return rate functions across various anisotropies and system sizes, and identify Loschmidt zeros in finite chains. Our analysis reveals distinct finite-size scaling of the Loschmidt echo at critical times with chain length and identifies the precise conditions on the anisotropy parameter governing the periodicity of the dynamical observables. In addition to the analytic study, we perform two types of numerical experiments on IBM-Q quantum devices. First, we use the Hadamard test to estimate the Bell-basis expansion coefficients and reconstruct the dynamical states, achieving accurate entanglement entropies and the Loschmidt echo for small systems. Second, we implement Trotter-error-free time-evolution circuits combined with randomized Pauli measurements. Post-processing via statistical correlations and classical shadows yields reliable estimates of the second-order R\'enyi entanglement entropy and the Loschmidt echo, showing satisfactory agreement with exact results.

Based on the strong-disorder renormalization group method, a microscopic mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain is proposed, which represents the annealing process as a gradual aggregation of strongly coupled spin clusters. The ferromagnetic ground state of clusters is either preserved or gets excited in pairwise fusions of clusters, depending on the effective annealing rate of the fusion, the latter events being responsible for the appearance of defects in the final state. A consequence of the theory is that, although the Griffiths-McCoy phases surrounding the critical point are gapless, they are still effectively gapped from the point of view of quantum annealing. Thereby we provide an explanation of the finiteness of gap outside of the critical point, which was implicit in an early approach to the problem by Kibble-Zurek scaling [Dziarmaga, Phys. Rev. B {\bf 74}, 064416 (2006)]. Furthermore, by identifying the accessible excitations, we refine the functional form of the vanishing of the gap at the critical point. The defect density in the final state is found to decrease with the annealing time $\tau$, as $n(\tau)\sim \ln^{-2}\left(\frac{\tau}{\ln^2\tau}\right)$ for large $\tau$. In addition to this, our approach gives access also to the density of defects at intermediate times of the annealing process.

Recent $\mu$SR experiments on elemental rhenium have shown that its superconducting phase spontaneously breaks time-reversal symmetry [1]. Ab initio calculations further indicate that finite antiferromagnetically ordered magnetic moments arise on the two atomic sites within the unit cell [2]. Furthermore, a mixture of spin singlet and triplet Cooper pairs best fits on the measured activated specific heat data. To elucidate these findings, we performed a comprehensive symmetry classification in the nonsymmorphic crystal structure and identified superconducting pairing parameters related to the observed symmetry breaking. We proposed a minimal underlying tight-binding and Bogoliubov-de Gennes model and listed some possible pairing mechanisms, which support the coexistence of superconductivity and magnetism, while discussing the role of the spin-orbit coupling and the nonsymmorphic structure. [1] T. Shang et al., Phys. Rev. Lett. 121, 257002 (2018) [2] G. Csire et al., Phys. Rev. B 106, L020501 (2022)

We study the spreading dynamics of an initially localized wave packet of finite norm in one-dimensional nonlinear Schrödinger lattices with random potentials. The problem has gained considerable interest in the literature, and it continues to attract attention due to its connection with the general properties of behavior of systems with the interplay between nonlinearity (often inducing self-focusing and correlations), dispersion/spreading and structural disorder. It is shown that adding small dielectric coupling to the ambient random medium results in asymptotic localization of the nonlinear field regardless of the Kerr nonlinearity strength. The nonlinear localization length is found to be $\Lambda_{\rm loc} \simeq \exp [(\pi / \varepsilon_r \tan\delta) \ln \beta]$, where $\tan\delta$ is the dielectric loss tangent, $\varepsilon_r$ is the relative permeability of the medium, and $\beta$ characterizes the Kerr nonlinearity. If the dielectric susceptibility is zero, then the nonlinear field undergoes sharp localization-delocalization transition above a certain critical value of the nonlinearity parameter. We then obtain this critical value using a topological mapping procedure onto a Cayley graph. The topological model predicts the possibility of self-induced localization when the "medium" to which the wave field is dielectrically coupled is the nonlinear wave itself. The mathematical methods, developed here, pave the way towards understanding the wave processes in complex media with competition between randomness, dispersiveness and nonlinearity, such as Anderson localization of a wave packet interacting with a disordered lattice structure.

The REOBiS2 (RE=rare-earth) family of layered chalcogenides exhibit remarkable functional properties, ranging from thermoelectricity to unconventional superconductivity. Recent studies reported that the superconducting properties of these materials can be improved and finely tuned following the novel high-entropy approach. We have studied the electronic structure of high-entropy REOBiS2 by combination of scanning photoemission microscopy (SPEM), angle-resolved photoemission spectroscopy (µ-ARPES), x-ray photoelectron spectroscopy (XPS) and soft-x-ray absorption spectroscopy (XAS) techniques. Apart from the intrinsic electronic inhomogeneities, revealed by SPEM, the XPS and XAS results have allowed us to correlate structural fluctuations, the mixed valence states and the Fermi surface properties finding a non-trivial relationship with the configurational entropy in REOBiS2.

We investigate the physics of fermions on a square lattice with π flux, subjected to disordered random Z2 gauge fields that arise from flux defects, i.e., plaquettes with zero flux. At half filling, where the system possesses BDI symmetry, we show that a new class of critical states is realized, with the states at zero energy showing a multifractal character that depends on the flux defect concentration c and local correlation between defects. For any concentration of flux defects, we find a nonfreezing multifractal spectrum with a tendency toward termination. We characterize this class of critical states by uncovering a robust relation between the conductivity and the Lyapunov exponent, which is satisfied by the states irrespective of the concentration or the local correlations between the flux defects. We demonstrate that renormalization group methods, based on perturbing the Dirac point, fail to capture this new class of critical states. This Letter not only offers new challenges to the theory of disordered systems in the chiral classes, but is also likely to be useful in understanding a variety of problems where fermions interact with discrete gauge fields.

Finding the ground state of an interacting quantum system is no- toriously difficult. In rare ‘exactly solvable’ cases, this can be done in a rigorous and manifest fashion. The Affleck-Kennedy-Lieb-Tasaki (AKLT) model is a famous example that shows ’fractionalization’, ‘symmetry-protected-topological’ properties and allows for elegant matrix product state (MPS) representation. It played a crucial historical role in understanding Haldane’s conjecture regarding the Heisenberg chain. Inspired by the AKLT model, we present exact solutions for a spin-1 chain with Kitaev-like couplings. We consider an expanded Kitaev model with bilinear and biquadratic terms. At an exactly solvable point, the Hamiltonian can be reexpressed as a sum of projection operators. Unlike the AKLT model, where projectors act on total spin, we project the component of spin along the bond direction. This leads to exponential ground state degeneracy, expressed in terms of fractionalized spin- 1/2 objects. This ‘fractionalized’ ground state space resembles a collection of non-interacting Ising spins, where each spin represents a ‘bond-conserved-quantity’. Using these ideas, we express ground-state wavefunctions as matrix product states, with explicit forms for all ground states. An exciting feature of our work is the combination of exact solvability and exponential degeneracy. We construct a phase diagram by varying the relative strength of bilinear and biquadratic terms. The fractionalized states provide a qualitative picture for the spin-1 Kitaev model, yielding approximate forms for the ground state and low-lying excitations.

We investigate an exactly solvable model for a non-unitary boundary conformal field theory (BCFT) in arbitrary dimensions $d$, defined by a Coulomb gas action involving the $Q$-curvature. This model serves as a natural CFT description for multifractality at Anderson transitions. By mapping multifractal operators to vertex primaries, we employ the $\alpha$-space conformal bootstrap to solve the boundary crossing equations. We derive exact, closed-form expressions for the bulk-to-boundary and boundary-to-boundary OPE coefficients. Our results characterize the complete spectrum of bulk and boundary primaries across various boundary conditions, providing an analytical framework for the surface multifractal spectrum. We further discuss the extension of these results to odd dimensions, offering a robust tool for probing boundary critical behavior in non-unitary systems.

We investigate correlated phases in twisted bilayer transition-metal dichalcogenides, focusing on moire systems as a tunable platform for strong correlations and emergent phenomena. An antiferromagnetic diagrammatic Gutzwiller variational framework with a perturbative expansion is developed to capture local correlation effects beyond standard mean-field approaches. Within this formalism, we study the emergence of antiferromagnetic order and analyze unconventional superconductivity. At present, the superconducting channel is evaluated at zeroth order without antiferromagnetic order, while ongoing work aims to incorporate their interplay. Our approach enables the evaluation of renormalized hopping processes, including both spin-conserving and spin-flip contributions, in realistic moire lattice geometries. The results provide insight into the microscopic mechanisms underlying correlated insulating states and superconductivity in twisted WSe$_2$.

The discovery of the Ce pyrochlores has re-energised the search for an experimental realisation of quantum spin ice, a fascinating U(1) quantum spin liquid model believed to realise aspects of strong-coupling QED. In this work, we address the oft-neglected effects nonmagnetic dilution on the proposed 3+1D emergent QED ground state of the spin liquid model. We deduce a mechanism by which the spins between pairs of nonmagnetic defects can be `frozen' into non-resonating singlets, potentially disrupting the spin liquid. This mechanism is relevant even at low levels of disorder -- even at 2% site dilution, ring exchange is a subleading correction for over 50% of the spins. We present Monte Carlo simulations of the proposed \textit{first order} perturbative model of the diluted QSI Hamiltonian, finding a large peak of heat capacity at an energy controlled by the transverse exchange. This model may be relevant to recent high resolution heat capacity measurements of Ce2Hf2O7.

A U(1) nonlinear sigma model (NLSM) with a one-dimensional temporal Berry phase term describes the critical theory of phase-fluctuation-driven superfluid (SF) transitions. We discuss that the temporal Berry phase leads to space-time anisotropic interference in vortex proliferation, resulting in a quasi-disordered phase characterized by short-range spatial order but persistent temporal phase coherence. This phase shares the essential SF phase correlation properties of the Bose Glass phase known from disordered boson systems, suggesting a unified topological origin for the emergence of the glassy phase in phase-fluctuation-driven superfluid transitions.

A central problem in cuprate physics is how superconductivity emerges from the spatially inhomogeneous normal state of a doped Mott insulator. We address this problem using finite-temperature tensor-network methods that access both thermodynamics and microscopic real-space structure. Using infinite projected entangled pair states, we find in the underdoped square-lattice Hubbard model a pronounced but finite maximum of the charge susceptibility near doping p~0.1, signalling strong incipient phase separation [1]. Minimally entangled typical thermal states snapshots show that this regime is governed by fluctuating hole-rich clusters embedded in antiferromagnetic backgrounds. These clusters generate large low-momentum charge fluctuations, but instead of evolving into macroscopic segregation they are forestalled by the onset of stripe order at lower temperature. We then analyze the t⁣-t'⁣-J model and show that superconducting correlations are localized on these hole-rich clusters [2]. At intermediate temperatures, pairing is fragmented across several localized singlet-pair modes associated with distinct hole clusters. As the temperature is lowered, these modes become increasingly aligned and extended, ultimately forming a coherent delocalized d-wave pattern. Finally, finite-temperature spectral functions obtained from dynamical METTS connect the melting of stripes to the filling of the pseudogap. Taken together, our results identify fluctuating charge clusters as the finite-temperature precursor from which both stripe order and coherent superconductivity develop. 1. A. Sinha and A. Wietek, Forestalled phase separation as the precursor to stripe order, Nat. Commun. 16, 10807 (2025). 2. A. Sinha, H. Karlsson, M. Ulaga, and A. Wietek, Evolution of superconductivity from charge clusters to stripes in the t-t'-J model, arXiv:2603.20368 [cond-mat.str-el] (2026). 3. M. Ulaga, A. Sinha, and A. Wietek, Filling the pseudogap by thermal melting of stripes in the t-t'-J model, manuscript in preparation (2026).

Non-Fermi liquids (NFLs) are metals that violate Landau’s Fermi liquid theory (FLT), lacking well-defined quasiparticles and exhibiting unusual scaling laws. For many years, achieving perturbative control of these systems has posed significant challenges, including Fermi surface patching, uncontrolled approximations, and hidden enhancements of ostensibly low-order diagrammatic contributions. Delacretaz et al. (2022) recast FLT as a bosonized effective field theory, arguing that, by restructuring the interactions, naive scaling can hold and a perturbative extension to NFLs is possible. We assess this argument by computing the one-loop perturbative structure of this NFL and find that, depending on the order in which limits are taken, either a familiar (though slightly unusual) Landau-damping regime emerges or a highly unusual regime appears in which the self-energy dominates and standard scaling breaks down. We offer interpretations of why this occurs and assess the viability of perturbative NFLs via bosonization as a whole.

We investigate interaction-induced altermagnetism in a minimal two-orbital model, following the effective framework introduced by Leeb et al. PRL 132, 236701 (2024). In this setting, symmetry-related orbitals act as an internal degree of freedom. Starting from an effective Hubbard-like interaction, we identify the orbital-selective spin order parameter responsible for the altermagnetic phase. Using the random phase approximation (RPA), we compute the particle–hole susceptibility and determine the critical temperature from its divergence. Our results demonstrate how orbital order drives altermagnetic behavior and establish the temperature scale for the onset of the phase, providing a transparent framework for altermagnetism without conventional sublattice symmetry breaking.

The spin-$1/2$ $J_1-J_2$-Heisenberg antiferromagnet on the square lattice is a paradigmatic system in quantum magnetism. While a Néel-ordered phase at small $J_2/J_1$ and a stripe-ordered phase at large $J_2/J_1$ are well established, the nature of the intermediate phase remains under debate. Numerical studies have reported conflicting results, proposing either a valence-bond solid phase or a possible $Z_2$ quantum spin liquid. In this work, we study the stability of a candidate $Z_2$ quantum spin liquid phase in this model using a fully self-consistent analytic approach. We first determine the mean-field parametrization of the system self-consistently and then incorporate fluctuation effects beyond mean field theory through an infinite resummation of interaction diagrams within the random phase approximation (RPA). Within the RPA, a collective low energy excitation emerges that allows us to assess the stability of the spin liquid state. At transitions toward magnetically ordered phases, this mode condenses at the corresponding ordering wavevector, whereas it remains gapped within the spin liquid regime. This approach further enables the calculation of the full finite-frequency spectral function, allowing for direct comparison with numerical methods such as variational Monte Carlo and density matrix renormalization group calculations, as well as experimental probes including inelastic neutron scattering.

Quantum spin liquids (QSLs) are long-range entangled phases of frustrated magnets exhibiting fractionalized spin excitations. In two dimensions, there is limited analytical understanding of their excitation spectra beyond parton mean-field theories, which fail to capture many features of the finite frequency dynamical response from recent experimental and numerical works. We use a self-consistent random phase approximation (RPA) for the J1-J2 Heisenberg model on the triangular lattice to describe the strong spinon-spinon interactions of the U(1) Dirac QSL. We obtain quantitative results for the dynamical spin structure factor and phase diagram compatible with comprehensive numerical efforts. We extend the method to chiral QSLs, and discuss its broad range of applicability to other models and for describing inelastic neutron scattering experiments.

I present our recent theoretical [1] and experimental [2] results on various effects of disorder in frustrated magnetic systems. 1. M. E. Zhitomirsky, V. B. Shenoy, and R. Moessner, Defect-induced spin textures in magnetic solids, Phys. Rev. B 111, 184414 (2025) 2. E. Riordan, E. Lhotel, N.-R. Camara, C. Marin, M. E. Zhitomirsky, Magnetocaloric Effect of Pure and Diluted Quantum Magnet Yb3Ga5O12, arXiv:2603.21922