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07:45 - 09:15
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Registration
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09:15 - 09:30
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Opening - Director Jan-Michael Rost & scientific coordinators
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Correlated Electrons - I
Chair: Frédéric Mila
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09:30 - 10:00
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Dieter Vollhardt
(Universität Augsburg, Germany)
From weak to extreme correlations in the Hubbard model
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.
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10:00 - 10:30
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Rok Zitko
(Jozef Stefan Institute, Slovenia)
Universal Magnetic Oscillations of dc Conductivity in the Incoherent Regime of Correlated Systems
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)
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10:30 - 11:00
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Tea/Coffee Break
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Correlated Electrons - II
Chair: H R Krishnamurthy
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11:00 - 11:30
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Michele Fabrizio
(SISSA - Scuola Internazionale Superiore di Studi Avanzati, Italy)
Fermi-liquid corrections and anomalous Hall phenomena
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.
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11:30 - 12:00
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Philip W. Phillips
(University of Illinois at Urbana-Champaign, USA)
Solving the Mott Problem
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.
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12:00 - 12:30
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Han Ma
(Stony Brook University, USA)
Fixed Points at Pomeranchuk/Stoner Instabilities
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.
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12:30 - 14:00
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Lunch
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Haerter-Shastry Magnetism
Chair: Jan Haerter
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14:00 - 14:30
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Cristian D. Batista
(University of Tennessee, USA)
Kinetic Energy Frustration as New Paradigm for Correlated Metals
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.
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14:30 - 15:00
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Claudio Castelnovo
(University of Cambridge, UK)
Spin-charge separation and resonant valence bond spin liquid in a kinetically-frustrated lightly-doped Mott insulator
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.
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15:00 - 15:30
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Hitesh Changlani
(Florida State University Tallahassee, USA)
Nagaoka and Haerter-Shastry kinetic magnetism in Hubbard systems
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.
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15:30 - 16:00
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Zhao Zhang
(University of Oslo, Norway)
RVB and Bethe Ansatz on Quasi-1D Lattices
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.
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16:00 - 16:30
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Colloquium Reception
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Colloquium Chair: Dieter Vollhardt
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16:30 - 17:30
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Colloquium: B. Sriram Shastry
(University of California, Santa Cruz, USA)
Outline of the Extremely Correlated Fermi Liquid Theory
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.
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17:30 - 18:00
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Free Discussion
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18:00 - 19:30
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Welcome Dinner
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