arXiv subjects

Gabriel Kotliar

Publications and source records attributed to Gabriel Kotliar.

At least 19 recordsLinked to original sources

arXiv2026

Interplay of spin-orbit coupling, crystal field splitting and correlations: a ghost rotationally invariant slave boson treatment

We investigate the interplay of spin-orbit coupling, crystal field splittings, and electronic correlations in the $t_{2g}$ Hubbard-Kanamori model within the recently formulated ghost rotationally invariant slave-boson method (GRISB). In particular, we study a tight binding model of Sr$_2$RuO$_4$ with parameters extracted from density functional theory and linearized quasiparticle self-consistent GW (LQSGW) calculations; we study the behavior of different physical quantities as the number of ghosts increases to examine the convergence of GRISB to dynamical mean field theory (DMFT) and experimental results; and we leverage the ability of GRISB to investigate the model over a wide range of parameters at low temperature. In particular, we examine both static and dynamical observables driven by the spin orbit coupling (SOC) and study how they vary as a function of the Hubbard $U$ and Hund's coupling $J$. GRISB converges quickly for most of these observables, and the calculations reveal the following: $U$ enhances the spin-orbit coupling while $J$ suppresses it. We also study the shape of the Fermi surface within different methodologies, and examine the Lifshitz transition which takes place as a function of strain in this material.

cond-mat.str-el↗

arXiv2026

Quantum criticality in the two-dimensional Hubbard model

We study the normal-state, doping-driven phase diagram of the square-lattice Hubbard model using the dynamical cluster approximation combined with the numerical renormalization group as a cluster solver, which gives direct access to real-frequency dynamics at essentially zero temperature. In a parameter regime relevant for cuprates, $U=7t$ and $t'=-0.3t$, we find a critical doping $p^{\ast}$ that marks a continuous quantum phase transition between a pseudogap metal and a normal Fermi liquid. The transition is identified by a continuous collapse, from both sides, of the Fermi-liquid scale extracted from charge, spin, and $d_{x^2-y^2}$-wave pairing susceptibilities. This collapse produces a non-Fermi-liquid regime at intermediate energy scales, which appears to extend to arbitrarily low scales at $p^{\ast}$. As $p^{\ast}$ is crossed from the normal Fermi liquid at $p>p^{\ast}$ into the pseudogap metal at $p<p^{\ast}$, the coherent low-energy spectral weight in the antinodal region is lost and replaced by a narrow, metallic pseudogap, while the nodal region evolves smoothly and remains comparatively coherent. This gives rise to Fermi arcs in the pseudogap metal at $p<p^{\ast}$, since the zero-frequency spectral weight remains large in the nodal region but is strongly suppressed in the antinodal region.

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arXiv2026

Dynamical scaling near the pseudogap quantum critical point of the two-dimensional Hubbard model

We study dynamical scaling in the quantum-critical fan of the pseudogap-metal to Fermi-liquid transition of the two-dimensional Hubbard model. Using a four-patch dynamical cluster approximation with the numerical renormalization group as a cluster impurity solver, we access real-frequency dynamics over several decades at arbitrary temperatures. Close to the critical doping, the local spin and cluster-current susceptibility spectra exhibit $x=\omega/T$ scaling of the form $\chi''(\omega,T)\sim \tanh(x/2)$, and the cluster contribution to the optical conductivity obeys $T\sigma'_{\mathrm{cl}}(\omega,T) \sim \tanh(x/2)/x$, implying a $1/T$ cluster dc conductivity. In the scaling regime, the vertex contribution to the cluster optical response is much larger than the bubble contribution. We further find evidence for a marginal-Fermi-liquid nodal self-energy. This, together with the $1/T$ vertex contribution to the conductivity, implies strange-metal optical transport in the quantum critical region. Our results describe several qualitative aspects of several experimental observations.

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arXiv2026

First-Principles Effective Mass in the Three-Dimensional Uniform Electron Gas

The quasiparticle effective mass $m^*$ of the three-dimensional uniform electron gas (UEG) is a fundamental Fermi-liquid parameter whose value and density dependence have remained controversial for decades. Using renormalized perturbation theory with explicit counterterms, we determine $m^*$ in the metallic regime ($r_s \le 6$) from first principles by two complementary routes -- the self-energy and the forward-scattering four-point vertex via the $p$-wave spin-symmetric Landau parameter $F_1^s$ -- that agree within uncertainties at each density through sixth renormalized order. The resulting $m^*/m$ remains close to unity throughout the metallic regime, with a shallow non-monotonic density dependence -- a minimum near $r_s\approx 1$ followed by a gentle upturn -- reflecting the interplay of exchange and dynamical screening in the self-energy, and disfavoring strong monotonic suppression. This finding supports a physical picture for the metallic UEG in which dominant charge correlations are concentrated in nearly forward scattering and generate only a weak $F_1^s$ component.

cond-mat.str-el↗

arXiv2026

QAssemble: A Pure Python Package for Quantum Many-Body Theory

QAssemble is a pure-Python package for the quantum many-body problem. It implements various functional approaches, such as tight-binding, Hartree-Fock, and GW approximations within a unified object-oriented architecture. Each physical concept--crystal structure, Hamiltonian, Green's function, self-energy, polarizability, screened Coulomb interaction--is represented as a distinct class. The modular design prioritizes code clarity and extensibility, leveraging NumPy, SciPy, and libdlr for numerical operations. Performance-critical kernels, including the polarizability bubble, Dyson equation inversion, and lattice Fourier transforms, are systematically vectorized and combined with the discrete Lehmann representation to achieve practical efficiency within a pure-Python environment. We validate QAssemble on the electronic structure of graphene with local and non-local interactions. Furthermore, benchmarks on a five-orbital extended Hund-Hubbard model demonstrate that this strategy delivers up to a 60x speedup over traditional loop-based Matsubara implementations. QAssemble supports both batch execution for production calculations and interactive workflows for method development.

cond-mat.str-el↗

arXiv2026

Unifying Variational and Dynamical Quantum Embedding: From Ghost Gutzwiller Approximation to Dynamical Mean-Field Theory

Dynamical and variational frameworks have long been viewed as distinct paradigms. In particular, in quantum embedding (QE) frameworks, dynamical mean-field theory (DMFT) captures nonperturbative dynamical correlations through a frequency-dependent self-energy, while the Gutzwiller approximation (GA) is formulated in terms of a variationally optimized ground-state wavefunction. Here we bridge these perspectives, proving that the ghost-Gutzwiller approximation (ghost-GA), which also admits a density-matrix-matching QE formulation known as ghost density matrix embedding theory (ghost-DMET), becomes strictly equivalent to DMFT in the limit of infinitely many auxiliary bath modes. This formal unification has immediate consequences. In particular, it yields a rigorous finite-temperature extension of ghost-GA and shows that the physical Green's function can be determined from static expectation values of the embedding Hamiltonians, providing a route to computational studies of competing phases in strongly correlated matter with DMFT-level accuracy, while bypassing the need to calculate dynamical spectra with conventional impurity solvers. More broadly, it shows that the variational ghost-GA, the density-matrix-matching ghost-DMET formulation, and the dynamical DMFT description are not separate constructions, but complementary formulations of the same QE structure, thereby providing a concrete formal basis for future controlled extensions beyond DMFT.

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arXiv2026

Pseudogapped Fermi liquids from emergent quasiparticles

We propose an interacting model that is exactly solvable in any spatial dimension and gives rise to a Fermi liquid (FL) featuring a pseudogapped (PG) single-particle spectral function and a vanishing quasiparticle (QP) weight at half-filling, without invoking Mott physics. The PG originates from a purely fermionic mechanism through emergent QPs arising from a correlated hopping interaction. By employing an appropriate coherent-state basis, we derive a Gaussian path-integral representation of the partition function, which enables systematic treatments of deviations from the Gaussian limit using standard many-body techniques, such as diagrammatic perturbation theory or mean-field theory. We explicitly demonstrate and discuss several properties of the exactly solvable limit on the square lattice, including the mechanism for temperature-dependent PG opening, the singular behavior of the self-energy, the violation of the Luttinger sum rule, and the role of Luttinger and Fermi surfaces. Finally, we explore quantum phase transitions between PG-FLs and Landau FLs.

cond-mat.str-el↗

arXiv2024

Deep Learning Based Superconductivity: Prediction and Experimental Tests

The discovery of novel superconducting materials is a longstanding challenge in materials science, with a wealth of potential for applications in energy, transportation, and computing. Recent advances in artificial intelligence (AI) have enabled expediting the search for new materials by efficiently utilizing vast materials databases. In this study, we developed an approach based on deep learning (DL) to predict new superconducting materials. We have synthesized a compound derived from our DL network and confirmed its superconducting properties in agreement with our prediction. Our approach is also compared to previous work based on random forests (RFs). In particular, RFs require knowledge of the chemical properties of the compound, while our neural net inputs depend solely on the chemical composition. With the help of hints from our network, we discover a new ternary compound $\textrm{Mo}_{20} \textrm{Re}_{6} \textrm{Si}_{4}$, which becomes superconducting below 5.4 K. We further discuss the existing limitations and challenges associated with using AI to predict and, along with potential future research directions.

cs.LG↗

arXiv2024

The Hund-metal path to strong electronic correlations

Atomic physics has a profound impact on the physical properties of correlated electron materials. This article describes a prime example of this phenomenon. We provide a non-technical introduction to the physics of Hund metals, a broad class of materials which include in particular iron pnictides and chalcogenides, as well as oxides of the 4d transition-metal series such as ruthenates. We highlight experiments which reveal distinctive signatures of Hund physics in selected materials. A key property of Hund metals is a clear separation between the energy and temperature scales associated with spin and orbital degrees of freedom. We emphasize the conceptual and practical importance of the non-perturbative renormalization group flow which identifies the relevant degrees of freedom at each energy scale. The flow begins with local atomic degrees of freedom at high energy, displays a universal behavior in the intermediate regime of spin-orbital separation and ends into a broad diversity of possible ordered phases. Ordering can take place either as an instability of the Fermi liquid regime with coherent quasiparticles or directly from the intermediate regime before Fermi liquid quasiparticles had a chance to emerge. Dynamical mean-field theory provides a natural conceptual framework as well as a powerful computational method to explain, calculate and predict many physical properties of correlated materials such as Hund metals. A copy-edited version of this article has been published (April, 2024) in Physics Today, 77(4), 46-53 (2024) \url{https://doi.org/10.1063/pt.wqrz.qpjx}

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arXiv2024

Tetragonal BaCoO$_3$: A Co$^{4+}$ Ferromagnetic Mott Insulator with Inverted Spin Crossover

The interplay between crystal electric field splitting of d states and Hund's rule exchange energy in cobalt-based perovskites offers a promising avenue for inducing spin-state transitions. This study reports a new body-centered tetragonal (BCT) phase of BaCoO$_3$ (BCT-BaCoO$_3$), synthesized under high pressure (15 GPa) and high temperature (1200 {\deg}C) conditions. BCT-BaCoO$_3$ adopts a double perovskite structure of EuTiO$_3$-type (space group I4/mcm, #140), confirmed by high-resolution scanning transmission electron microscopy. X-ray photoelectron spectroscopy reveals a rare Co$^{4+}$ valence state. Magnetization and X-ray absorption measurements reveal a low-spin to high-spin transition that takes place between 200 and 300 K. While spin crossovers are relatively common among common oxides, the one observed in BCT-BaCoO$_3$ is remarkable in that it proceeds in the opposite direction from conventional spin transitions. BCT-BaCoO$_3$ exhibits a low-spin (S = 1/2) state at high temperatures and transitions to a high-spin (S = 5/2) state at low temperatures. Within the high-spin state, hard ferromagnetic order onsets at T$_C$ = 107 K. Electrical resistivity indicates weak magnetoresistance and insulating behavior. Overall, BCT-BaCoO$_3$ presents an exceptional model for the exploration of spin-state transitions and the study of Co spin states in cobalt-based perovskites.

cond-mat.mtrl-sci↗

arXiv2024

Charge self-consistent density functional theory plus ghost rotationally-invariant slave-boson theory for correlated materials

We present a charge self-consistent density functional theory combined with the ghost-rotationally-invariant slave-boson (DFT+gRISB) formalism for studying correlated materials. This method is applied to SrVO$_3$ and NiO, representing prototypical correlated metals and charge-transfer insulators. For SrVO$_3$, we demonstrate that DFT+gRISB yields an accurate equilibrium volume and effective mass close to experimentally observed values. Regarding NiO, DFT+gRISB enables the simultaneous description of charge transfer and Mott-Hubbard bands, significantly enhancing the accuracy of the original DFT+RISB approach. Furthermore, the calculated equilibrium volume and spectral function reasonably agree with experimental observations.

cond-mat.str-el↗

arXiv2024

Dynamical scaling and Planckian dissipation due to heavy-fermion quantum criticality

We study dynamical scaling associated with a Kondo-breakdown quantum critical point (KB-QCP) of the periodic Anderson model, treated by two-site cellular dynamical mean-field theory (2CDMFT). In the quantum critical region, the staggered spin exhibits SYK-like slow dynamics and its dynamical susceptibility shows $ω/T$ scaling. We propose a scaling Ansatz that describes this behavior. It also implies Planckian dissipation for the longest-lived excitations. The current susceptibility follows the same scaling ansatz, leading to strange-metal scaling. This demonstrates that the KB-QCP described by 2CDMFT is an intrinsic (i.e., disorder-free) strange-metal fixed point. Surprisingly, the SYK-like dynamics and scaling are driven by strong vertex contributions to the susceptibilities. Our results for the optical conductivity match experimental observations on YbRh${}_2$Si${}_2$ and CeCoIn${}_5$.

cond-mat.str-el↗

arXiv2024

Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials

We assess the accuracy of the ghost-rotationally-invariant slave-boson (g-RISB) theory in multiorbital systems by applying it to both the three-orbital degenerate Hubbard model and a realistic Sr2RuO4 model extracted from first principle simulations, and comparing the results to those obtained using the dynamical mean-field theory (DMFT). Our findings indicate that g-RISB's accuracy can be systematically improved toward the exact DMFT limit in infinite dimensional multiorbital models by increasing the number of ghost orbitals. This allows for a more precise description of aspects of Hund metal physics and Mott physics compared to the original RISB approach. We also demonstrate that g-RISB reliably captures the quasiparticle weights, Fermi surface, and low-energy spectral function for the realistic Sr2RuO4 model compared to DMFT. Moreover, we showcase the potential of using the density matrix renormalization group method as an impurity solver within the g-RISB framework to study systems with a larger number of ghost orbitals. These results show the potential of g-RISB as a reliable tool for simulating correlated materials. The connection between the g-RISB and DMFT self-energy is also discussed.

cond-mat.str-el↗

arXiv2023

Low-energy perspective on two-orbital Hund metals and the case of LaNiO2

The Hund-metal route to strong correlations continues to attract large interest in the condensed-matter community. The question arose to what extent it applies to the infinite-layer nickelates and, as a related question, to two-orbital systems in general. Here, we provide a low-energy perspective on this topic through a dynamical mean-field study using the numerical renormalization group (NRG) as a real-frequency impurity solver. We find that the RG flow from high to low energy is a uniquely adequate tool to reveal two-stage Kondo screening (2SKS), a fascinating mechanism for Hund physics. Further, we show that 2SKS takes place in a quarter-filled two-orbital system, but can be easily suppressed by a sufficiently large crystal-field splitting. We apply these insights to LaNiO2 using a recently proposed two-orbital model and show that it is indeed the crystal-field splitting that suppresses multiorbital phenomena in this scenario. Our general findings open the way for further explorations of 2SKS, and we propose a way of reviving low-energy Hund physics in LaNiO2 by counteracting the crystal field.

cond-mat.str-el↗

arXiv2023

Vacancy-induced tunable Kondo effect in twisted bilayer graphene

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo-screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Ab-initio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wavefunctions at the magic angle. We argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.

cond-mat.str-el↗

arXiv2023

Emergent Properties of the Periodic Anderson Model: a High-Resolution, Real-Frequency Study of Heavy-Fermion Quantum Criticality

We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory, with the numerical renormalization group (NRG) as an impurity solver. The PAM describes an itinerant $c$ band hybridizing with a localized $f$ band. At $T=0$, it exhibits a hybridization tuned Kondo breakdown quantum critical point (KB-QCP) from a Kondo to an RKKY phase. At the KB-QCP, the $f$ band changes character from itinerant to mainly localized, while the $c$ band remains itinerant. We elucidate its nature in detail by performing a high-resolution, real-frequency study of dynamical quantities. NRG allows us to study the quantum critical non-Fermi-liquid (NFL) regime located between $T_{FL}<T_{NFL}$. Surprisingly, self-consistency is essential to stabilize the NFL and the QCP. The Fermi-liquid (FL) scale $T_{FL}$ decreases towards and vanishes at the QCP. At $T=0$, we find the following properties. The $f$ quasiparticle (QP) weight $Z_f$ decreases continuously as the QCP is approached from either side, vanishing only at the QCP. Therefore, $Z_f$ is nonzero in both the Kondo and the RKKY phase; hence, the FL QP comprise $c$ and $f$ electrons in both phases. The Fermi surface (FS) volumes in the two phases differ. Whereas the large-FS Kondo phase has a usual two-band structure, the small-FS RKKY phase has an unexpected three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and the RKKY phase. The FS reconstruction is accompanied by the appearance of a Luttinger surface (LS) on which the $f$ self-energy diverges. The FS and LS volumes are related to the density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent LS as evidence for $f$-electron fractionalization in the RKKY phase. Our Hall coefficient and specific heat are in good qualitative agreement with experiment.

cond-mat.str-el↗

arXiv2023

ComDMFT v.2.0: Fully Self-Consistent ab initio GW+EDMFT for the Electronic Structure of Correlated Quantum Materials

ComDMFT is a parallel computational package designed to study the electronic structure of correlated quantum materials from first principles. Our approach is based on the combination of first-principles methods and dynamical mean field theories. In version 2.0, we implemented fully-diagrammatic GW+EDMFT from first-principles. In this approach, correlated electrons are treated within full GW+EDMFT and the rest are treated within full-GW, seamlessly. This implementation enables the electronic structure calculation of quantum materials with weak, intermediate, and strong electron correlation without prior knowledge of the degree of electron correlation.

cond-mat.str-el↗

arXiv2023

Softening of $dd$ excitation in the resonant inelastic x-ray scattering spectra as a signature of Hund's coupling in nickelates

We investigate the effects of Hund's coupling on the resonant X-ray absorption spectra of the recently discovered family of layered nickelate superconductors. We contrast two scenarios depending on the relative strength of the ratio of the effective Hund's coupling ($J_H$) to the crystal fields ($\Delta$) in these systems. We carry out the cluster and DFT+DMFT simulations of the RIXS signal at the Ni $L$-edge for different values of Hund's coupling. We find the latter dominates for the parent compound while the former becomes important for sufficiently large doping. Our results are consistent with the observations of a softening of a RIXS peak as a function of doping by Rossi {\sl et al.}~\cite{PhysRevB.104.L220505}, only when the Hund coupling is sizeable. To interpret the results, we separate the theoretical RIXS signal into spin conserving and non-spin conserving channels and conclude that the infinite layer nickelates are in a regime where $\Delta$ and $J$ compete effectively and suggest further experimental tests of the theory.

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