arXiv subjects

Antoine Georges

Publications and source records attributed to Antoine Georges.

At least 19 recordsLinked to original sources

arXiv2026

Superconductivity in the $t$-$t'$ Hubbard Model from Symmetry-Preserving Neural-Network Quantum States

Despite its fundamental importance in the theory of strongly correlated electrons, the nature of the ground state of the two-dimensional doped Hubbard model remains intensely debated. Variational approaches provide a powerful route to this problem, but their conclusions can depend sensitively on the chosen wave-function parameterization, the mean-field initialization, or the pinning fields used to guide the optimization, as well as on boundary conditions. This can favor one type of symmetry breaking over another, making it difficult to distinguish the genuine interplay of intertwined or competing orders from biases induced by the variational parameterization. Here, we introduce the Symmetry-Preserving Backflow Pairing (SBP) ansatz, a neural-network wave function that respects translational symmetry by construction and thereby avoids these broken-symmetry minima. The SBP ansatz reaches state-of-the-art variational energies for the $t$-$t'$ Hubbard model on lattices up to $24\times24$ with $504$ electrons, below those of competing pure stripe solutions. By extrapolating to the thermodynamic limit, we find robust evidence for $d$-wave superconducting order, resolving a long-standing question about the $1/8$-doped model at $t'/t=-0.2$ and $U/t=8.0$. Built on general principles of symmetry and locality, the SBP wave function provides a broadly applicable variational representation for challenging interacting fermionic systems.

cond-mat.str-el↗

arXiv2026

Scaling Laws for Neural-Network Quantum States

Scaling laws, the power-law relations between loss, architecture size, and compute observed in modern neural networks, offer a quantitative way to characterize the complexity of a learning problem, with the exponent governing the decay of the loss reflecting how rapidly additional resources translate into improved accuracy, and thus how hard the target is to learn. Whether an analogous framework can characterize the complexity of physical problems remains open. We address this question for Neural-Network Quantum States, a leading variational approach for strongly correlated quantum many-body systems. Using transformer wave functions to approximate ground states of the $J_1$-$J_2$ Heisenberg model on triangular and square lattices with up to $20\times 20$ sites, we find that the $V$-score, a measure of accuracy of a variational state, decays as a power law in training compute. Under an appropriate rescaling of compute, results for different system sizes collapse onto a single curve, analogous to scaling collapse in critical phenomena. The resulting power law is, to a good approximation, independent of the number of sites, showing that the transformer Ansatz is size-consistent for the systems considered. The exponent decreases systematically with frustration, identifying it as a quantitative measure of representational difficulty of the ground state and establishing scaling laws as a general framework for benchmarking variational ans\"{a}tze.

cond-mat.dis-nn↗

arXiv2026

Emergence of spin entanglement with the pseudogap onset in the Fermi-Hubbard model

Despite decades of intense theoretical and experimental investigation, the two-dimensional Fermi-Hubbard model still resists a complete microscopic understanding. Conventional approaches typically probe global observables and locally resolved correlation functions. Here, we develop a complementary perspective based on the measurement of entanglement. Using both an ultracold-atom quantum simulator and numerical simulations based on the dynamical vertex approximation, we find that entanglement is closely tied to the onset of the enigmatic pseudogap regime: spin-singlet entanglement emerges only as the pseudogap sets in and, in contrast to classical correlations, remains confined to nearest-neighbour sites in this regime. Our results, therefore, disfavour purely classical-fluctuation theories of the pseudogap and constrain microscopic models to those that develop nearest-neighbour spin-singlet entanglement at the pseudogap onset.

cond-mat.str-el↗

arXiv2026

Revealing Hund superdispersion with tunneling spectroscopy

In cuprate superconductors, electron-electron repulsion results in characteristic spectroscopic features known as `waterfalls', where the sharp quasiparticle dispersion transitions into broad Hubbard bands. However, in multi-orbital systems, the additional Hund coupling results in behavior that defies the conventional Mott--Hubbard paradigm, creating qualitatively distinct `superdispersive' features in the spectral function. Here, we use tunneling spectroscopy to reveal this signature of Hund physics in Sr$_2$RuO$_4$. By combining density functional theory, dynamical mean-field theory, and continuum local density of states calculations, we show that the experimental features are in excellent agreement with theoretical predictions and intimately linked to the non-monotonous energy dependence of the real part of the self-energy in a Hund metal. Our results provide direct experimental evidence for Hund-induced spectroscopic features and open a new route to probing correlation effects in quantum materials.

cond-mat.str-el↗

arXiv2026

Beyond Variational Bias: Resolving Intertwined Orders in the Hubbard Model

The two-dimensional Hubbard model at finite doping hosts competing or intertwined orders, resulting in conflicting conclusions from different computational approaches regarding its ground state. We show that a key source of such discrepancies is the bias encoded in the variational ansatz. We consider three different Transformer backflow fermionic wave functions based on a Slater determinant, its particle-hole counterpart, and a Pfaffian, initialized without any mean-field pretraining. We show that, despite achieving nearly degenerate, state-of-the-art variational energies, each ansatz converges to a state with qualitatively different spin, charge, and pairing correlations. Upon improving accuracy via symmetry restoration and variance reduction, however, all three converge to the same physical picture: coexisting superconducting and stripe orders. These results demonstrate that variational energy alone is insufficient to identify the ground state in the presence of competing phases, and highlight the importance of tracking how correlation functions evolve as the wave function is systematically improved before drawing physical conclusions.

cond-mat.str-el↗

arXiv2026

Neural-Network Quantum Embedding Solvers for Correlated Materials

Quantum impurity solvers are the computational bottleneck of quantum embedding approaches to correlated materials, such as dynamical mean-field theory (DMFT). We show that neural networks trained on synthetic, material-agnostic data learn the impurity mapping from hybridization functions and local interactions to Green's functions with quantitative accuracy for both model systems and real materials, providing fast solvers for single- and multi-orbital models. Benchmarks against numerically controlled quantum Monte Carlo show that the method reproduces the Mott transition, multi-orbital phase diagrams of Hubbard-Kanamori models, and the electronic properties of SrVO$_3$ and SrMnO$_3$. The learned solvers achieve orders-of-magnitude speedup and can initialize controlled calculations, dramatically accelerating DMFT while preserving accuracy.

cond-mat.str-el↗

arXiv2026

Electronic correlations and dynamical screening with ab initio quantum embedding

First-principles descriptions of correlated quantum materials require a simultaneous treatment of strong local many-body effects and nonlocal dynamical screening. We present an efficient fully self-consistent implementation of $GW$+EDMFT that combines nonlocal effects at the $GW$ level with a non-perturbative treatment of local correlations within extended dynamical mean-field theory (EDMFT), while providing a controlled double-counting prescription. Crucially, self-consistency in both the Green's function and the dynamically screened interaction is essential to achieve a consistent description of screening processes across energy scales. The efficient computation of this self-consistent solution is enabled here by compressing two-particle correlation functions using interpolative separable density fitting (ISDF). Applying the scheme to the Mott insulator SrMnO$_3$ and the correlated metal LaNiO$_3$, we show that full self-consistency resolves the overscreening inherent to constrained-RPA approaches. By suppressing spurious low-energy screening channels, a Mott-insulating state in quantitative agreement with experiment is obtained for SrMnO$_3$. These results establish fully self-consistent $GW$+EDMFT as a predictive ab initio framework for strongly correlated quantum materials.

cond-mat.str-el↗

arXiv2026

Simulating superconductivity in mixed-dimensional $t_\parallel$-${J}_\parallel$-${J}_\perp$ bilayers with neural quantum states

Motivated by the recent discovery of superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$ (LNO) under pressure, we study a mixed-dimensional (mixD) bilayer $t_\parallel$-$J_\parallel$-$J_\perp$ model, which has been proposed as an effective low-energy description of LNO. Using neural quantum states (NQS), and in particular Gutzwiller-projected Hidden Fermion Pfaffian State, we access the ground-state properties on large lattices up to $8\times 8\times 2$ sites. We show that this model exhibits superconductivity across a wide range of dopings and couplings, and analyze the pairing behavior in detail. We identify a crossover from tightly bound, Bose-Einstein-condensed interlayer pairs at strong interlayer exchange to more spatially extended Bardeen-Cooper-Schrieffer-like pairs as the interlayer exchange is decreased. Furthermore, upon tuning the intralayer exchange, we observe a sharp transition from interlayer $s$-wave pairing to intralayer $d$-wave pairing, consistent with a first-order change in the pairing symmetry. We verify that our simulations are accurate by comparing with matrix product state simulations on coupled ladders. Our results represent the first simulation of a fermionic multi-orbital system with NQS, and provide the first evidence for superconductivity in two-dimensonal bilayers using high-precision numerics. These findings provide insight into superconductivity in bilayer nickelates and cold atom quantum simulation platforms.

cond-mat.str-el↗

arXiv2025

Impact of strong electronic correlations on altermagnets: the case of NiS2

One of the distinguishing features of an altermagnet is that its spin-up and spin-down bands display a nodal momentum-dependent splitting even in the absence of spin-orbit coupling. While this property has been investigated in many weakly-correlated altermagnetic materials, the impact of strong electron-electron interactions on the spin-dependent electronic structure has remained little explored, particularly in metals. Here, we propose NiS2 as a prototypical strongly correlated metallic altermagnet. While at ambient pressure this compound is an altermagnetic Mott insulator, it undergoes a pressure-driven metal-insulator transition (MIT) while maintaining its altermagnetic ordered phase. By systematically comparing DFT, DFT+U, and DFT+DMFT calculations on the metallic altermagnetic phase near the MIT, we disentangle how strong static and dynamic correlations modify the electronic structure. Specifically, the spin splitting of the bands is modified not only through the enhancement of the local magnetic moment caused by static correlations, but also by the momentum-dependent bandwidth renormalization caused by dynamic correlations. Moreover, dynamic electronic correlations cause a pronounced lifetime asymmetry between the spin-up and spin-down quasiparticles, an effect that is amplified by the particle-hole asymmetry promoted by Hund's correlations. Our results not only shed light on the rich landscape of correlation effects in metallic altermagnets, but also establishes NiS2 as a platform to investigate the interplay between Mott and Hund physics and altermagnetic order.

cond-mat.str-el↗

arXiv2025

Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states

Whether the ground state of the square lattice Hubbard model exhibits superconductivity remains a major open question, central to understanding high temperature cuprate superconductors and ultra-cold fermions in optical lattices. Numerical studies have found evidence for stripe-ordered states and superconductivity at strong coupling but the phase diagram remains controversial. Here, we show that one can resolve the subtle energetics of metallic, superconducting, and stripe phases using a new class of neural quantum state (NQS) wavefunctions that extend hidden fermion determinant states to Pfaffians. We simulate several hundred electrons using fast Pfaffian algorithms allowing us to measure off-diagonal long range order. At strong coupling and low hole-doping, we find that a non-superconducting filled stripe phase prevails, while superconductivity coexisting with partially-filled stripes is stabilized by a negative next neighbor hopping t-prime, with |t-prime| > 0.1. At larger doping levels, we introduce momentum-space correlation functions to mitigate finite size effects that arise from weakly-bound pairs. These provide evidence for uniform d-wave superconductivity at U = 4, even when t-prime = 0. Our results highlight the potential of NQS approaches, and provide a fresh perspective on superconductivity in the square lattice Hubbard model.

cond-mat.supr-con↗

arXiv2025

Expert Evaluation of LLM World Models: A High-$T_c$ Superconductivity Case Study

Large Language Models (LLMs) show great promise as a powerful tool for scientific literature exploration. However, their effectiveness in providing scientifically accurate and comprehensive answers to complex questions within specialized domains remains an active area of research. Using the field of high-temperature cuprates as an exemplar, we evaluate the ability of LLM systems to understand the literature at the level of an expert. We construct an expert-curated database of 1,726 scientific papers that covers the history of the field, and a set of 67 expert-formulated questions that probe deep understanding of the literature. We then evaluate six different LLM-based systems for answering these questions, including both commercially available closed models and a custom retrieval-augmented generation (RAG) system capable of retrieving images alongside text. Experts then evaluate the answers of these systems against a rubric that assesses balanced perspectives, factual comprehensiveness, succinctness, and evidentiary support. Among the six systems two using RAG on curated literature outperformed existing closed models across key metrics, particularly in providing comprehensive and well-supported answers. We discuss promising aspects of LLM performances as well as critical short-comings of all the models. The set of expert-formulated questions and the rubric will be valuable for assessing expert level performance of LLM based reasoning systems.

cond-mat.supr-con↗

arXiv2025

Insulating transport in anisotropic metals: breakdown of Drude transport and the puzzling $c$-axis resistivity of Sr$_2$RuO$_4$ and other layered oxides

We reveal a mechanism that may explain the non-metallic out-of-plane resistivity in layered metals. By carefully examining how the Drude-Boltzmann expression for the $c$-axis conductivity emerges out of the Kubo formula, we find, besides the standard metallic term proportional to the carrier lifetime $\tau$, a non-Drude contribution proportional to $1/\tau$. The Drude behavior breaks down when $1/\tau > 2 \eta^*$, the crossover value $\eta^*$ being small (and hence observable) when the $c$-axis velocities vary rapidly with the distance from the Fermi surface. We consider the Hund metal Sr$_2$RuO$_4$ as a test case, which we study within a realistic dynamical mean-field theory approach. The non-Drude behavior observed experimentally in $c$-axis transport is reproduced and explained by our considerations, showing that earlier invoked extrinsic mechanisms that involve either impurities or phonons are unnecessary. We point out that the small value of $\eta^*$ is due to a peculiar accidental cancellation due to destructive interference characteristic of body-centered tetragonal lattices.

cond-mat.str-el↗

arXiv2025

Double descent: When do neural quantum states generalize?

Neural quantum states (NQS) provide flexible and compact wavefunction parameterizations for numerical studies of quantum many-body physics. In particular, NQS aim to circumvent the exponential scaling of the Hilbert space by compressing quantum many-body wavefunctions with a tractable amount of parameters. While inspired by deep learning, it remains unclear to what extent NQS share characteristics with neural networks used for standard machine learning tasks. We demonstrate that, in a simplified supervised setting, NQS exhibit the double descent phenomenon, a key feature of modern deep learning, where generalization worsens as network size increases before improving again in an overparameterized regime. Notably, we find the second descent to occur only for network sizes much larger than the Hilbert space dimension, i.e. network sizes that are out of reach for problems of practical interest. Within our setting, this observation places typical NQS in the underparameterized regime. We also observe that the optimal network size in the underparameterized regime depends on the number of unique training samples. While the double descent phenomenon does indeed translate to the NQS setting, potential practical consequences of our findings point more towards the need for symmetry-aware, physics-informed architecture design, rather than directly adopting machine learning heuristics.

cond-mat.dis-nn↗

arXiv2025

Neural Network-Augmented Pfaffian Wave-functions for Scalable Simulations of Interacting Fermions

Developing accurate numerical methods for strongly interacting fermions is crucial for improving our understanding of various quantum many-body phenomena, especially unconventional superconductivity. Recently, neural quantum states have emerged as a promising approach for studying correlated fermions, highlighted by the hidden fermion and backflow methods, which use neural networks to model corrections to fermionic quasiparticle orbitals. In this work, we expand these ideas to the space of Pfaffians, a wave-function that naturally expresses superconducting pairings, and propose the hidden fermion Pfaffian state (HFPS), which flexibly represents both unpaired and superconducting phases and scales to large systems with favorable asymptotic complexity. In our numerical experiments, HFPS provides state-of-the-art variational accuracy in different regimes of both the attractive and repulsive Hubbard models. We show that the HFPS is able to capture both s-wave and d-wave pairing, and therefore may be a useful tool for modeling phases with unconventional superconductivity.

cond-mat.str-el↗

arXiv2025

Site-polarized Mott phases competing with a correlated metal in twisted WSe$_2$

Twisted WSe$_2$ hosts superconductivity, metal-insulator phase transitions, and field-controllable Fermi-liquid to non-Fermi-liquid transport properties. In this work, we use dynamical mean-field theory to provide a coherent understanding of the electronic correlations shaping the twisted WSe$_2$ phase diagram. We find a correlated metal competing with three distinct site-polarized correlated insulators; the competition is controlled by interlayer potential difference and interaction strength. The insulators are characterized by a strong differentiation between orbitals with respect to carrier concentration and effective correlation strength. Upon doping, a strong particle-hole asymmetry emerges, resulting from a Zaanen-Sawatzky-Allen-type charge-transfer mechanism. The associated charge-transfer physics and proximity to a van Hove singularity in the correlated metal sandwiched between two site-polarized insulators naturally explains the interlayer potential-driven metal-to-insulator transition, particle-hole asymmetry in transport, and the coherence-incoherence crossover in $3.65^\circ$ twisted WSe$_2$.

cond-mat.str-el↗

arXiv2025

Electron-phonon origins of unconventional resistivity in moderately correlated perovskite oxides

Transition-metal perovskite oxides exhibit moderately correlated metallic phases, several of which exhibit a $T^2$ resistivity scaling up to temperatures far exceeding the regime where Fermi-liquid electron-electron scattering is expected to dominate. Some of these materials, such as SrMoO$_3$, also exhibit unexplained ultra-low room-temperature resistivity. We demonstrate that in SrMoO$_3$, SrWO$_3$, SrTaO$_3$, SrNbO$_3$, and SrVO$_3$ electron-phonon scattering results in quadratic-scaling resistivity due to the shape of the Fermi surface and the thermal activation of optical phonons. We also reveal that the origin of the low resistivity of SrMoO$_3$ is an overall low electron-phonon coupling strength, and identify SrWO$_3$ and SrTaO$_3$ as other possible low-resistivity oxides. Additionally, we find that the strength of electron-phonon coupling is sensitive to structural distortions, energies of optical phonons, and the treatment of electronic correlations. This suggests design principles for finding other ultra-high conductivity transition-metal oxides, and has significant implications for theoretical interpretation of direct-current resistivity in transition-metal oxides and beyond.

cond-mat.mtrl-sci↗

arXiv2025

Low-temperature transport in high-conductivity correlated metals: a density-functional plus dynamical mean-field study of cubic perovskites

While methods based on density-functional perturbation theory have dramatically improved our understanding of electron-phonon contributions to transport in materials, methods for accurately capturing electron-electron scattering relevant to low temperatures have seen significantly less development. The case of high-conductivity, moderately correlated materials characterized by low scattering rates is particularly challenging, since exquisite numerical precision of the low-energy electronic structure is required. Recent methodological advancements to density-functional theory combined with dynamical mean-field theory (DFT+DMFT), including adaptive Brillouin-zone integration and numerically precise self-energies, enable a rigorous investigation of electron-electron scattering in such materials. In particular, these tools may be leveraged to perform a robust scattering-rate analysis on both real- and imaginary-frequency axes. Applying this methodology to a subset of ABO$_3$ perovskite oxides -- SrVO$_3$, SrMoO$_3$, PbMoO$_3$, and SrRuO$_3$ -- we demonstrate its ability to qualitatively and quantitatively describe electron-electron contributions to the temperature-dependent direct-current resistivity. This combination of numerical techniques offers fundamental insight into the role of electronic correlations in transport phenomena and provides a predictive tool for identifying materials with potential for technological applications.

cond-mat.mtrl-sci↗

arXiv2025

Hund flat band in a frustrated spinel oxide

Electronic flat bands associated with quenched kinetic energy and heavy electron mass have attracted great interest for promoting strong electronic correlations and emergent phenomena such as high-temperature charge fractionalization and superconductivity. Intense experimental and theoretical research has been devoted to establishing the rich non-trivial metallic and heavy fermion phases intertwined with such localized electronic states. Here, we investigate the transition metal oxide spinel LiV2O4, an enigmatic heavy fermion compound lacking localized f orbital states. We use angle-resolved photoemission spectroscopy and dynamical mean field theory to reveal a new kind of correlation-induced flat band with suppressed inter-atomic electron hopping arising from intra-atomic Hund coupling. The appearance of heavy quasiparticles is ascribed to a proximate orbital-selective Mott state characterized by fluctuating local moments as evidenced by complementary magnetotransport measurements. The spectroscopic fingerprints of long-lived quasiparticles and their disappearance with increasing temperature further support the emergence of a high-temperature bad metal state observed in transport data. This work resolves a long-standing puzzle on the origin of heavy fermion behavior and unconventional transport in LiV2O4. Simultaneously, it opens a new path to achieving flat bands through electronic interactions in d-orbital systems with geometrical frustration, potentially enabling the realization of exotic phases of matter such as the fractionalized Fermi liquids.

cond-mat.str-el↗