arXiv subjects

Antoine Georges

Publications and source records attributed to Antoine Georges.

At least 73 records · Page 4Linked to original sources

arXiv2021

Charge self-consistent electronic structure calculations with dynamical mean-field theory using Quantum ESPRESSO, Wannier90 and TRIQS

We present a fully charge self-consistent implementation of dynamical mean field theory (DMFT) combined with density functional theory (DFT) for electronic structure calculations of materials with strong electronic correlations. The implementation uses the Quantum ESPRESSO package for the density functional theory calculations, the Wannier90 code for the up-/downfolding and the TRIQS software package for setting up and solving the DMFT equations. All components are available under open source licenses, are MPI-parallelized, fully integrated in the respective packages, and use an hdf5 archive interface to eliminate file parsing. We show benchmarks for three different systems that demonstrate excellent agreement with existing DFT+DMFT implementations in other ab-initio electronic structure codes.

cond-mat.str-el↗

arXiv2021

Mott insulating states with competing orders in the triangular lattice Hubbard model

The physics of the triangular lattice Hubbard model exhibits a rich phenomenology, ranging from a metal-insulator transition, intriguing thermodynamic behavior, and a putative spin liquid phase at intermediate coupling, ultimately becoming a magnetic insulator at strong coupling. In this multimethod study, we combine a finite-temperature tensor network method, minimally entangled thermal typical states (METTS), with two Green-function-based methods, connected-determinant diagrammatic Monte Carlo and cellular dynamical mean-field theory, to establish several aspects of this model. We elucidate the evolution from the metallic to the insulating regime from the complementary perspectives brought by these different methods. We compute the full thermodynamics of the model on a width-four cylinder using METTS in the intermediate to strong coupling regime. We find that the insulating state hosts a large entropy at intermediate temperatures, which increases with the strength of the coupling. Correspondingly, and consistently with a thermodynamic Maxwell relation, the double occupancy has a minimum as a function of temperature which is the manifestation of the Pomeranchuk effect of increased localization upon heating. The intermediate coupling regime is found to exhibit both pronounced chiral as well as stripy antiferromagnetic spin correlations. We propose a scenario in which time-reversal symmetry-broken states compete with stripy-spin states at lowest temperatures.

cond-mat.str-el↗

arXiv2021

Planckian Metal at a Doping-Induced Quantum Critical Point

We numerically study a model of interacting spin-$1/2$ electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi liquid phase with a large Fermi surface volume and a low-doping phase with local moments ordering into a spin-glass. We show that this quantum critical point has non-Fermi liquid properties characterized by $T$-linear Planckian behavior, $ω/T$ scaling and slow spin dynamics of the Sachdev-Ye-Kitaev (SYK) type. The $ω/T$ scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a `skewed' non-Fermi liquid.

cond-mat.str-el↗

arXiv2021

Skewed Non-Fermi Liquids and the Seebeck Effect

We consider non-Fermi liquids in which the inelastic scattering rate has an intrinsic particle-hole asymmetry and obeys $ω/T$ scaling. We show that, in contrast to Fermi liquids, this asymmetry influences the low-temperature behaviour of the thermopower even in the presence of impurity scattering. Implications for the unconventional sign and temperature dependence of the thermopower in cuprates in the strange metal (Planckian) regime are emphasized.

cond-mat.str-el↗

arXiv2021

Machine learning band gaps from the electron density

A remarkable consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of an injective map between the electronic density and any observable of the many electron problem in an external potential. In this work, we study the problem of predicting a particular observable, the band gap of semiconductors and band insulators, from the knowledge of the local electronic density. Using state-of-the-art machine learning techniques, we predict the experimental band gaps from computationally inexpensive density functional theory calculations. We propose a modified Behler-Parrinello (BP) architecture that greatly improves the model capacity while maintaining the symmetry properties of the BP architecture. Using this scheme, we obtain band gaps at a level of accuracy comparable to those obtained with state of the art and computationally intensive hybrid functionals, thus significantly reducing the computational cost of the task.

cond-mat.dis-nn↗

arXiv2021

Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature

The interplay between thermal and quantum fluctuations controls the competition between phases of matter in strongly correlated electron systems. We study finite-temperature properties of the strongly coupled two-dimensional doped Hubbard model using the minimally-entangled typical thermal states (METTS) method on width $4$ cylinders. We discover that a phase characterized by commensurate short-range antiferromagnetic correlations and no charge ordering occurs at temperatures above the half-filled stripe phase extending to zero temperature. The transition from the antiferromagnetic phase to the stripe phase takes place at temperature $T/t \approx 0.05$ and is accompanied by a step-like feature of the specific heat. We find the single-particle gap to be smallest close to the nodal point at $\mathbf{k}=(π/2, π/2)$ and detect a maximum in the magnetic susceptibility. These features bear a strong resemblance to the pseudogap phase of high-temperature cuprate superconductors. The simulations are verified using a variety of different unbiased numerical methods in the three limiting cases of zero temperature, small lattice sizes, and half-filling. Moreover, we compare to and confirm previous determinantal quantum Monte Carlo results on incommensurate spin-density waves at finite doping and temperature.

cond-mat.str-el↗

arXiv2021

Correlation-Induced Octahedral Rotations in SrMoO$_3$

Distortions of the oxygen octahedra influence the fundamental electronic structure of perovskite oxides, such as their bandwidth and exchange interactions. Utilizing a fully ab-initio methodology based on density functional theory plus dynamical mean field theory (DFT+DMFT), we study the crystal and magnetic structure of SrMoO$_3$. Comparing our results with DFT+$U$ performed on the same footing, we find that DFT+$U$ overestimates the propensity for magnetic ordering, as well as the octahedral rotations, leading to a different ground state structure. This demonstrates that structural distortions can be highly sensitive to electronic correlation effects, and to the considered magnetic state, even in a moderately correlated metal such as SrMoO$_3$. Moreover, by comparing different downfolding schemes, we demonstrate the robustness of the DFT+DMFT method for obtaining structural properties, highlighting its versatility for applications to a broad range of materials.

cond-mat.str-el↗

arXiv2021

Inter-orbital singlet pairing in Sr$_2$RuO$_4$: a Hund's superconductor

We study the superconducting gap function of Sr$_2$RuO$_4$. By solving the linearized Eliashberg equation with a correlated pairing vertex extracted from a dynamical mean-field calculation we identify the dominant pairing channels. An analysis of the candidate gap functions in orbital and quasiparticle band basis reveals that an inter-orbital singlet pairing of even parity is in agreement with experimental observations. It reconciles in particular the occurrence of a two-component order parameter with the presence of line-nodes of quasiparticles along the c-axis in the superconducting phase. The strong angular dependence of the gap along the Fermi surface is in stark contrast to its quasi-locality when expressed in the orbital basis. We identify local inter-orbital spin correlations as the driving force for the pairing and thus reveal the continuation of Hund's physics into the superconducting phase.

cond-mat.str-el↗

arXiv2021

Quantum phase transition at non-zero doping in a random $t$-$J$ model

We present exact diagonalization results on finite clusters of a $t$-$J$ model of spin-1/2 electrons with random all-to-all hopping and exchange interactions. We argue that such random models capture qualitatively the strong local correlations needed to describe the cuprates and related compounds, while avoiding lattice space group symmetry breaking orders. The previously known spin glass ordered phase in the insulator at doping $p=0$ extends to a metallic spin glass phase up to a transition $p=p_c \approx 1/3$. The dynamic spin susceptibility shows signatures of the spectrum of the Sachdev-Ye-Kitaev models near $p_c$. We also find signs of the phase transition in the entropy, entanglement entropy and compressibility, all of which exhibit a maximum near $p_c$. The electron energy distribution function in the metallic phase is consistent with a disordered extension of the Luttinger-volume Fermi surface for $p>p_c$, while this breaks down for $p<p_c$.

cond-mat.str-el↗

arXiv2021

Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model

The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as a testing ground, we perform a comparative study of a comprehensive set of state of the art quantum many-body methods. Upon cooling into its insulating antiferromagnetic ground-state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate temperature metallic regime and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations. We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo) serving as a benchmark. By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes. Based on this analysis, we explain how quasiparticles can coexist with increasingly long-range antiferromagnetic correlations, and why dynamical mean-field theory is found to provide a remarkably accurate approximation of local quantities in the metallic regime. We also critically discuss whether imaginary time methods are able to capture the non-Fermi liquid singularities of this fully nested system.

cond-mat.str-el↗

arXiv2021

Moiré heterostructures as a condensed matter quantum simulator

Twisted van der Waals heterostructures have latterly received prominent attention for their many remarkable experimental properties, and the promise that they hold for realising elusive states of matter in the laboratory. We propose that these systems can, in fact, be used as a robust quantum simulation platform that enables the study of strongly correlated physics and topology in quantum materials. Among the features that make these materials a versatile toolbox are the tunability of their properties through readily accessible external parameters such as gating, straining, packing and twist angle; the feasibility to realize and control a large number of fundamental many-body quantum models relevant in the field of condensed-matter physics; and finally, the availability of experimental readout protocols that directly map their rich phase diagrams in and out of equilibrium. This general framework makes it possible to robustly realize and functionalize new phases of matter in a modular fashion, thus broadening the landscape of accessible physics and holding promise for future technological applications.

quant-ph↗

arXiv2021

On the Spatial Locality of Electronic Correlations in LiFeAs

We address the question of the degree of spatial non-locality of the self energy in the iron-based superconductors, a subject which is receiving considerable attention. Using LiFeAs as a prototypical example, we extract the self energy from angular-resolved photoemission spectroscopy (ARPES) data. We use two distinct electronic structure references: density functional theory in the local density approximation and linearized quasiparticle self consistent GW (LQSGW). We find that with the LQSGW reference, spatially local dynamical correlations provide a consistent description of the experimental data, and account for some surprising aspects of the data such as the substantial out of plan dispersion of the electron Fermi surface having dominant xz/yz character. Hence, correlations effects can be separated into static non-local contributions well described by LQSGW and dynamical local contributions. Hall effect and resistivity data are shown to be consistent with this description.

cond-mat.str-el↗

arXiv2020

The Hubbard model on the Bethe lattice via variational uniform tree states: metal-insulator transition and a Fermi liquid

We numerically solve the Hubbard model on the Bethe lattice with finite coordination number $z=3$, and determine its zero-temperature phase diagram. For this purpose, we introduce and develop the `variational uniform tree state' (VUTS) algorithm, a tensor network algorithm which generalizes the variational uniform matrix product state algorithm to tree tensor networks. Our results reveal an antiferromagnetic insulating phase and a paramagnetic metallic phase, separated by a first-order doping-driven metal-insulator transition. We show that the metallic state is a Fermi liquid with coherent quasiparticle excitations for all values of the interaction strength $U$, and we obtain the finite quasiparticle weight $Z$ from the single-particle occupation function of a generalized "momentum" variable. We find that $Z$ decreases with increasing $U$, ultimately saturating to a non-zero, doping-dependent value. Our work demonstrates that tensor-network calculations on tree lattices, and the VUTS algorithm in particular, are a platform for obtaining controlled results for phenomena absent in one dimension, such as Fermi liquids, while avoiding computational difficulties associated with tensor networks in two dimensions. We envision that future studies could observe non-Fermi liquids, interaction-driven metal-insulator transitions, and doped spin liquids using this platform.

cond-mat.str-el↗

arXiv2020

Deep learning the Hohenberg-Kohn maps of Density Functional Theory

A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of a bijection between the local density and the ground-state many-body wave function. Here we study the problem of constructing approximations to the Hohenberg-Kohn map using a statistical learning approach. Using supervised deep learning with synthetic data, we show that this map can be accurately constructed for a chain of one-dimensional interacting spinless fermions, in different phases of this model including the charge ordered Mott insulator and metallic phases and the critical point separating them. However, we also find that the learning is less effective across quantum phase transitions, suggesting an intrinsic difficulty in efficiently learning non-smooth functional relations. We further study the problem of directly reconstructing complex observables from simple local density measurements, proposing a scheme amenable to statistical learning from experimental data.

cond-mat.dis-nn↗

arXiv2020

Nonlinear spectroscopy of collective modes in excitonic insulator

The nonlinear optical response of an excitonic insulator coupled to lattice degrees of freedom is shown to depend in strong and characteristic ways on whether the insulating behavior originates primarily from electron-electron or electron-lattice interactions. Linear response optical signatures of the massive phase mode and the amplitude (Higgs) mode are identified. Upon nonlinear excitation resonant to the phase mode, a new in-gap mode at twice the phase mode frequency is induced, leading to a huge second harmonic response. Excitation of in-gap phonon modes leads to different and much smaller effects. A Landau-Ginzburg theory analysis explain these different behavior and reveals that a parametric resonance of the strongly excited phase mode is the origin of the photo-induced mode in the electron-dominant case. The difference in the nonlinear optical response serve as a measure of the dominant mechanism of the ordered phase.

cond-mat.str-el↗

arXiv2020

Nature of symmetry breaking at the excitonic insulator transition: Ta$_2$NiSe$_5$

Ta$_2$NiSe$_5$ is one of the most promising materials for hosting an excitonic insulator ground state. While a number of experimental observations have been interpreted in this way, the precise nature of the symmetry breaking occurring in Ta$_2$NiSe$_5$, the electronic order parameter, and a realistic microscopic description of the transition mechanism are, however, missing. By a symmetry analysis based on first-principles calculations, we uncover the \emph{discrete} lattice symmetries which are broken at the transition. We identify a purely electronic order parameter of excitonic nature that breaks these discrete crystal symmetries and contributes to the experimentally observed lattice distortion from an orthorombic to a monoclinic phase. Our results provide a theoretical framework to understand and analyze the excitonic transition in Ta$_2$NiSe$_5$ and settle the fundamental questions about symmetry breaking governing the spontaneous formation of excitonic insulating phases in solid-state materials.

cond-mat.mtrl-sci↗

arXiv2020

Electromagnetic coupling in tight-binding models for strongly correlated light and matter

We discuss the construction of low-energy tight-binding Hamiltonians for condensed matter systems with a strong coupling to the quantum electromagnetic field. Such Hamiltonians can be obtained by projecting the continuum theory on a given set of Wannier orbitals. However, different representations of the continuum theory lead to different low-energy formulations, because different representations may entangle light and matter, transforming orbitals into light-matter hybrid states before the projection. In particular, a multi-center Power-Zienau-Woolley transformation yields a dipolar Hamiltonian which incorporates the light-matter coupling via both Peierls phases and a polarization density. We compare this dipolar gauge Hamiltonian and the straightforward Coulomb gauge Hamiltonian for a one-dimensional solid, to describe sub-cycle light-driven electronic motion in the semiclassical limit, and a coupling of the solid to a quantized cavity mode which renormalizes the band-structure into electron-polariton bands. Both descriptions yield the same result when many bands are taken into account, but the dipolar Hamiltonian is more accurate when the model is restricted to few electronic bands, while the Coulomb Hamiltonian requires fewer electromagnetic modes.

cond-mat.str-el↗

arXiv2020

Deconfined critical point in a doped random quantum Heisenberg magnet

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interactions between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a non-zero critical value $p_c$ of the hole doping $p$ away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point $p_c$ is flanked by confining phases: a disordered Fermi liquid with carrier density $1+p$ for $p>p_c$, and a metallic spin glass with carrier density $p$ for $p<p_c$. Additional evidence for the critical behavior is obtained from a large $M$ analysis of a model which extends the SU(2) spin symmetry to SU($M$). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.

cond-mat.str-el↗