arXiv subjects

A. -M. S. Tremblay

Publications and source records attributed to A. -M. S. Tremblay.

At least 37 records · Page 2Linked to original sources

arXiv2023

Dynamical Variational Monte Carlo as a quantum impurity solver: Application to Cluster Dynamical Mean-Field Theory

Two of the primary sources of error in the Cluster dynamical mean-field theory (CDMFT) technique arise from the use of finite size clusters and finite size baths, which makes the development of impurity solvers that can treat larger systems an essential goal. In this work we introduce an impurity solver based on the recently developed dynamical variational Monte Carlo (dVMC) method. Variational Monte Carlo possesses a favorable scaling as a function of system size, which enables the treatment of systems beyond the reach of current exact diagonalization solvers. To benchmark the technique, we perform a systematic set of CDMFT calculations on the one-dimensional Hubbard model. We compare to results obtained with an exact diagonalization solver for small clusters, and against the exact solution in the thermodynamic limit obtained by Lieb and Wu for larger clusters. The development of improved impurity solvers will help extend the reach of quantum cluster methods, which can be applied to a wide range of strongly-correlated electron systems, promising new insights on their emergent behavior.

cond-mat.str-el↗

arXiv2023

An Improved Two-Particle Self-Consistent Approach

The two-particle self-consistent approach (TPSC) is a method for the one-band Hubbard model that can be both numerically efficient and reliable. However, TPSC fails to yield physical results deep in the renormalized classical regime of the bidimensional Hubbard model where the spin correlation length becomes exponentially large. We address the limitations of TPSC with improved approaches that we call TPSC+ and TPSC+SFM. In this work, we show that these improved methods satisfy the Mermin-Wagner theorem and the Pauli principle. We also show that they are valid in the renormalized classical regime of the 2D Hubbard model, where they recover a generalized Stoner criterion at zero temperature in the antiferromagnetic phase. We discuss some limitations of the TPSC+ approach with regards to the violation of the f-sum rule and conservation laws, which are solved within the TPSC+SFM framework. Finally, we benchmark the TPSC+ and TPSC+SFM approaches for the one-band Hubbard model in two dimensions and show how they have an overall better agreement with available diagrammatic Monte Carlo results than the original TPSC approach.

cond-mat.str-el↗

arXiv2023

Mott transition, Widom line and pseudogap in the half-filled triangular lattice Hubbard model

The Mott transition is observed experimentally in materials that are magnetically frustrated so that long-range order does not hide the Mott transition at finite temperature. The Hubbard model on the triangular lattice at half-filling is a paradigmatic model to study the interplay of interactions and frustration on the normal-state phase diagram. We use the dynamical cluster approximation with continuous time auxiliary field quantum Monte Carlo to solve this model for 1, 4, 6, 12, and 16 site clusters with detailed analysis performed for the 6 site cluster. We show that a) for every cluster there is an inflection point in the double occupancy as a function of interaction, defining a Widom line that extends above the critical point of the first-order Mott transition; b) the presence of this line and the cluster size dependence argue for the observability of the Mott transition at finite temperature in the thermodynamic limit; c) the loss of spectral weight in the metal to Mott insulator transition as a function of temperature and for strong interactions is momentum dependent, the hallmark of a pseudogap. That pseudogap spans a large region of the phase diagram near the Mott transition.

cond-mat.str-el↗

arXiv2023

Nonlocal corrections to dynamical mean-field theory from the two-particle self-consistent method

Theoretical methods that are accurate for both short-distance observables and long-wavelength collective modes are still being developed for the Hubbard model. Here, we benchmark an approach that combines dynamical mean-field theory (DMFT) observables with the two-particle self-consistent theory (TPSC). This offers a way to include non-local correlations in DMFT while also improving TPSC. The benchmarks are published diagrammatic quantum Monte Carlo results for the two-dimensional square lattice Hubbard model with nearest-neighbor hopping. This method (TPSC+DMFT) is relevant for weak to intermediate interaction, satisfies the local Pauli principle and allows us to compute a spin susceptibility that satisfies the Mermin-Wagner theorem. The DMFT double occupancy determines the spin and charge vertices through local spin and charge sum rules. The TPSC self-energy is also improved by replacing its local part with the local DMFT self-energy. With this method, we find improvements for both spin and charge fluctuations and for the self-energy. We also find that the accuracy check developed for TPSC is a good predictor of deviations from benchmarks for this model. TPSC+DMFT can be used in regimes where quantum Monte Carlo is inaccessible. In addition, this method paves the way to multi-band generalizations of TPSC that could be used in advanced electronic structure codes that include DMFT.

cond-mat.str-el↗

arXiv2022

Prediction of anomalies in the velocity of sound for the pseudogap of hole-doped cuprates

We predict sound anomalies at the doping $δ_{p}$ where the pseudogap ends in the normal state of hole-doped cuprates. Our prediction is based on the two-dimensional compressible Hubbard model using cluster dynamical mean-field theory. We find sharp anomalies (dips) in the velocity of sound as a function of doping and interaction. These dips are a signature of supercritical phenomena, stemming from an electronic transition without symmetry breaking below the superconducting dome. If experimentally verified, these signatures may help to solve the fundamental question of the nature of the pseudogap -- pinpointing its origin as due to Mott physics and resulting short-range correlations.

cond-mat.str-el↗

arXiv2022

Fermi Arcs From Dynamical Variational Monte Carlo

Variational Monte Carlo is a many-body numerical method that scales well with system size. It has been extended to study the Green function only recently by Charlebois and Imada (2020). Here we generalize the approach to systems with open boundary conditions in the absence of translational invariance. Removing these constraints permits the application of embedding techniques like Cluster perturbation theory (CPT). This allows us to solve an enduring problem in the physics of the pseudogap in cuprate high-temperature superconductors, namely the existence or absence of Fermi arcs in the one-band Hubbard model. We study the behavior of the Fermi surface and of the density of states as a function of hole doping for clusters of up to 64 sites, well beyond the reach of modern exact diagonalization solvers. We observe that the technique reliably captures the transition from a Mott insulator at half filling to a pseudogap, evidenced by the formation of Fermi arcs, and finally to a metallic state at large doping. The ability to treat large clusters with quantum cluster methods helps to minimize potential finite size effects and enables the study of systems with long range orders, which will help extend the reach of these already powerful methods and provide important insights on the nature of various strongly correlated many-electron systems, including the high-T$_c$ cuprate superconductors.

cond-mat.str-el↗

arXiv2022

Disorder effects on hot spots in electron-doped cuprates

Antiferromagnetic fluctuations in two dimensions cause a decrease in spectral weight at so-called hot spots associated with the pseudogap in electron-doped cuprates. In the 2D Hubbard model, these hot spots occur when the Vilk criterion is satisfied, namely when the spin correlation length exceeds the thermal de Broglie wavelength. Using the two-particle self-consistent approach, here we show that this criterion may be violated near the antiferromagnetic quantum critical point when sufficient disorder is added to the model. Static disorder decreases inelastic scattering, in contradiction with Matthiessen's rule, leading to a shift in the position of the quantum critical point and a modification of the conditions for the appearance of hot spots. This opens the road to a study of the interplay between disorder, antiferromagnetic fluctuations and superconductivity in electron-doped cuprates.

cond-mat.str-el↗

arXiv2021

Resilient Fermi liquid and strength of correlations near an antiferromagnetic quantum critical point

Near the antiferromagnetic quantum critical point (QCP) of electron-doped cuprate superconductors, angle-resolved photoemission experiments detect hot spots where the Fermi surface disappears. Here we demonstrate, using the two-particle self-consistent theory, that in the antinodal region the Fermi liquid remains stable for a broad range of angles on the Fermi surface and for all dopings near the QCP. We show how the quasiparticle weight Z and effective mass m* change and then abruptly become meaningless as the hot spots are approached. We propose a dimensionless number, easily accessible in ARPES experiments, that can be used to gauge the strength of correlations.

cond-mat.str-el↗

arXiv2021

Non-Fermi liquid phase and linear-in-temperature scattering rate in overdoped two dimensional Hubbard model

Understanding electronic properties that violate the Landau Fermi liquid paradigm in cuprate superconductors remains a major challenge in condensed matter physics. The strange metal state in overdoped cuprates that exhibits linear-in-temperature scattering rate and dc resistivity is a particularly puzzling example. Here, we compute the electronic scattering rate in the two-dimensional Hubbard model using cluster generalization of dynamical mean-field theory. We present a global phase diagram documenting an apparent non-Fermi liquid phase, in between the pseudogap and Fermi liquid phase in the doped Mott insulator regime. We discover that in this non-Fermi liquid phase, the electronic scattering rate $γ_k(T)$ can display linear temperature dependence as temperature $T$ goes to zero. In the temperature range that we can access, the $T-$ dependent scattering rate is isotropic on the Fermi surface, in agreement with recent experiments. Using fluctuation diagnostic techniques, we identify antiferromagnetic fluctuations as the physical origin of the $T-$ linear electronic scattering rate.

cond-mat.str-el↗

arXiv2021

Fermi arcs vs hole pockets: periodization of a cellular two-band model

It is still debated whether the low-doping Fermi surface of cuprates is composed of hole pockets or of disconnected Fermi arcs. Results from cellular dynamical mean field theory (c-DMFT) support the Fermi arcs hypothesis by predicting corresponding Fermi arcs for the Hubbard model. Here, we introduce a simple parametrization of the self-energy, in the spirit of Yang-Rice-Zhang theory, and show that state of the art c-CDMFT calculations cannot give a definitive answer to the question of Fermi arcs vs holes pockets, and this, independently of the periodization (cumulant or Green's function) used to display spectral weights of the infinite lattice. Indeed, when our model is restricted to a cluster and periodized like in c-DMFT, only two adjustable parameters suffice to reproduce the qualitative details of the frequency and momentum dependence of the low energy c-DMFT spectral weight for both periodizations. In other words, even though our starting model has a Fermi surface composed of hole and electron pockets, it leads to Fermi arcs when restricted to a cluster and periodized like in c-DMFT. We provide a new "compact tiling" scheme to recover the hole and electron pockets of our starting non-interacting lattice model, suggesting that better periodization schemes might exist.

cond-mat.str-el↗

arXiv2021

Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator

A key open issue in condensed matter physics is how quantum and classical correlations emerge in an unconventional superconductor from the underlying normal state. We study this problem in a doped Mott insulator with information theory tools on the two-dimensional Hubbard model at finite temperature with cluster dynamical mean-field theory. We find that the local entropy detects the superconducting state and that the difference in the local entropy between the superconducting and normal states follows the same difference in the potential energy. We find that the thermodynamic entropy is suppressed in the superconducting state and monotonically decreases with decreasing doping. The maximum in entropy found in the normal state above the overdoped region of the superconducting dome is obliterated by superconductivity. The total mutual information, which quantifies quantum and classical correlations, is amplified in the superconducting state of the doped Mott insulator for all doping levels, and shows a broad peak versus doping, as a result of competing quantum and classical effects.

cond-mat.str-el↗

arXiv2021

Oxygen hole content, charge-transfer gap, covalency, and cuprate superconductivity

Experiments have shown that the families of cuprate superconductors that have the largest transition temperature at optimal doping also have the largest oxygen hole content at that doping. They have also shown that a large charge-transfer gap, a quantity accessible in the normal state, is detrimental to superconductivity. We solve the three-band Hubbard model with cellular dynamical mean-field theory and show that both of these observations follow from the model. Cuprates play a special role amongst doped charge-transfer insulators of transition metal oxides because copper has the largest covalent bonding with oxygen.

cond-mat.supr-con↗

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↗

arXiv2020

Potential energy contribution to the thermopower of correlated electrons

Certain classes of strongly correlated systems promise high thermopower efficiency, but a full understanding of correlation effects on the Seebeck coefficient is lacking. This is partly due to limitations of Boltzmann-type approaches. One needs a formula for the thermopower that allows separate investigations of the kinetic and potential energy contributions to the evolution with temperature and doping of the thermopower. Here we address this issue by deriving for Hubbard-like interactions a formula for the thermopower that separates the potential from the kinetic energy contribution and facilitates a better understanding of correlation effects on the Seebeck coefficient. As an example, the thermopower of the one-band Hubbard model is calculated from dynamical mean-field. For interactions in both the intermediate and strong correlation limit, the contributions from kinetic and potential energy nearly cancel.

cond-mat.str-el↗

arXiv2020

Entanglement and classical correlations at the doping-driven Mott transition in the two-dimensional Hubbard model

Tools of quantum information theory offer a new perspective to characterize phases and phase transitions in interacting many-body quantum systems. The Hubbard model is the archetypal model of such systems and can explain rich phenomena of quantum matter with minimal assumptions. Recent measurements of entanglement-related properties of this model using ultracold atoms in optical lattices hint that entanglement could provide the key to understanding open questions of the doped Hubbard model, including the remarkable properties of the pseudogap phase. These experimental findings call for a theoretical framework and new predictions. Here we approach the doped Hubbard model in two dimensions from the perspective of quantum information theory. We study the local entropy and the total mutual information across the doping-driven Mott transition within plaquette cellular dynamical mean-field theory. We find that upon varying doping these two entanglement-related properties detect the Mott insulating phase, the strongly correlated pseudogap phase, and the metallic phase. Imprinted in the entanglement-related properties we also find the pseudogap to correlated metal first-order transition, its finite temperature critical endpoint, and its supercritical crossovers. Through this footprint we reveal an unexpected interplay of quantum and classical correlations. Our work shows that sharp variation in the entanglement-related properties and not broken symmetry phases characterizes the onset of the pseudogap phase at finite temperature.

cond-mat.str-el↗

arXiv2020

Interaction and temperature effects on the magneto-optical conductivity of Weyl liquids

Negative magnetoresistance is one of the manifestations of the chiral anomaly in Weyl semimetals. The magneto-optical conductivity also shows transitions between Landau levels that are not spaced as in an ordinary electron gas. How are such topological properties modified by interactions and temperature? We answer this question by studying a lattice model of Weyl semimetals with an on-site Hubbard interaction. Such an interacting Weyl semimetal, dubbed as Weyl liquid, may be realized in Mn$_3$Sn. We solve that model with single-site dynamical mean-field theory. We find that in a Weyl liquid, quasiparticles can be characterized by a quasiparticle spectral weight $Z$, although their lifetime increases much more rapidly as frequency approaches zero than in an ordinary Fermi liquid. The negative magnetoresistance still exists, even though the slope of the linear dependence of the DC conductivity with respect to the magnetic filed is decreased by the interaction. At elevated temperatures, a Weyl liquid crossesover to bad metallic behavior where the Drude peak becomes flat and featureless.

cond-mat.str-el↗

arXiv2020

Mott transition and high-temperature crossovers at half-filling

The interaction-driven Mott transition in the half-filled Hubbard model is a first-order phase transition that terminates at a critical point $(T_\mathrm{c},U_\mathrm{c})$ in the temperature-interaction plane $T-U$. A number of crossovers occur along lines that extend for some range above $(T_\mathrm{c},U_\mathrm{c})$. Asymptotically close to $(T_\mathrm{c},U_\mathrm{c})$, these lines coalesce into the so-called Widom line. The existence of $(T_\mathrm{c},U_\mathrm{c})$ and of the associated crossovers becomes unclear when long-wavelength fluctuations or long-range order occur above $(T_\mathrm{c},U_\mathrm{c})$. We study this problem using continuous-time quantum Monte Carlo methods as impurity solvers for both Dynamical Mean-Field Theory (DMFT) and Cellular Dynamical Mean-Field Theory (CDMFT). We contrast the cases of the square lattice, where antiferromagnetic fluctuations dominate in the vicinity of the Mott transition, and the triangular lattice where they do not. The inflexion points and maxima found near the Widom line for the square lattice can serve as proxy for the triangular lattice case. But the only crossover observable in all cases at sufficiently high temperature is that associated with the opening of the Mott gap. The same physics also controls an analog crossover in the resistivity called the "Quantum Widom line".

cond-mat.str-el↗

arXiv2020

Analysis of the magnetic and magnetocaloric properties of ALaFeMnO6 (A= Sr, Ba and Ca) double perovskites

In previous studies, we have reported that double perovskite La2NiMnO6 presents a non-negligible potential for room temperature magnetocaloric tasks. With the aim of improving even further the cooling performances and the working temperature range of double perovskites, we report the magnetic and magnetocaloric properties of La2MnFeO6 and ALaMnFeO6 (A = Sr, Ba, Ca) compounds. X-ray diffraction (XRD) and Rietveld refinement show that La2MnFeO6 (LMFO) and CaLaMnFeO6 (CLMFO) samples crystallize in an orthorhombic structure with the Pnma space group. However, a rhombohedral structure with the R3C space group is obtained for BaLaMnFeO6 (BLMFO) and SrLaMnFeO6 (SLMFO) samples. Substituting La by Ba or Sr in LMFO leads to a clear increase of the Curie temperature (Tc) compared to LMFO from 150 K for BLMFO up to 350 K for SLMFO. Moreover, CLMFO shows the smallest Tc down to 70 K. Ferromagnetic-like behavior is observed for SLMFO and BLMFO while CLMFO's magnetism resembles that of LMFO. A clear connection between the structural parameters and the magnetic properties of these doped LMFO samples is unveiled as the highest Tc and the largest magnetization are observed for SLMFO which shows also bond angles closest to 180° and the smallest bond lengths, thus optimizing the superexchange interaction. The partial substitution of Sr for La leads in fact to a significant magnetocaloric effect over a wide operating temperature range extending beyond 300 K. For some optimal growth conditions, its entropy change varies slowly over an unusually large temperature range, which is of clear interest from a practical point of view.

cond-mat.mtrl-sci↗