arXiv subjects

A. -M. S. Tremblay

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

At least 73 records · Page 4Linked to original sources

arXiv2017

Maximum entropy analytic continuation for frequency-dependent transport coefficients with non-positive spectral weight

The computation of transport coefficients, even in linear response, is a major challenge for theoretical methods that rely on analytic continuation of correlations functions obtained numerically in Matsubara space. While maximum entropy methods can be used for certain correlation functions, this is not possible in general, important examples being the Seebeck, Hall, Nernst and Reggi-Leduc coefficients. Indeed, positivity of the spectral weight on the positive real-frequency axis is not guaranteed in these cases. The spectral weight can even be complex in the presence of broken time-reversal symmetry. Various workarounds, such as the neglect of vertex corrections or the study of the infinite frequency or Kelvin limits have been proposed. Here, we show that one can define auxiliary response functions that allow to extract the desired real-frequency susceptibilities from maximum entropy methods in the most general multiorbital cases with no particular symmetry. As a benchmark case, we study the longitudinal thermoelectric response and corresponding Onsager coefficient in the single-band two-dimensional Hubbard model treated with dynamical mean-field theory (DMFT) and continuous-time quantum Monte Carlo (CTQMC). We thereby extend to transport coefficients the maximum entropy analytic continuation with auxiliary functions (MaxEntAux method), developed for the study of the superconducting pairing dynamics of correlated materials.

cond-mat.str-el↗

arXiv2016

Density Waves Cause Sub-Gap Structures but no Pseudogap in Superconducting Cuprates

In scanning tunneling microscopy (STM) conductance curves, the superconducting gap of cuprates is sometimes accompanied by small sub-gap structures at very low energy. This was documented early on near vortex cores and later at zero magnetic field. Using mean-field toy models of coexisting d-wave superconductivity ($d$SC), \emph{d}-form factor density wave ($d$FF-DW), and extended s-wave pair density wave ($s'$PDW), we find agreement with this phenomenon, with $s'$PDW playing a critical role. We explore the high variability of the gap structure with changes in band structure and density wave (DW) wave vector, thus explaining why sub-gap structures may not be a universal feature in cuprates. In the absence of nesting, non-superconducting results never show signs of pseudogap, even for large density waves magnitudes, therefore reinforcing the idea of a distinct origin for the pseudogap, beyond mean-field theory. Therefore, we also briefly consider the effect of DWs on a pre-existing pseudogap.

cond-mat.supr-con↗

arXiv2016

Antagonistic effects of nearest-neighbor repulsion on the superconducting pairing dynamics in the doped Mott insulator regime

The nearest-neighbor superexchange-mediated mechanism for d_{x^2-y^2}-wave superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion $U=9t$ and nearest-neighbor repulsion $V=0,2t,4t$. In the underdoped regime, $V$ increases the CDMFT superconducting transition temperature $T_c^d$ even though it decreases the superconducting order parameter at low temperature for all dopings. However, $V$ decreases $T_c^d$ in the overdoped regime. We gain insight into these paradoxical results through a detailed study of the frequency dependence of the anomalous spectral function, extracted at finite temperature via the MaxEntAux method for analytic continuation. A systematic study of dynamical positive and negative contributions to pairing reveals that even though $V$ has a high-frequency depairing contribution, it also has a low frequency pairing contribution since it can reinforce superexchange through $J=4t^2/(U-V)$. Retardation is thus crucial to understand pairing in doped Mott insulators, as suggested by previous zero-temperature studies. We also comment on the tendency to charge order for large $V$ and on the persistence of d-wave superconductivity over extended-$s$ or s+d-wave.

cond-mat.supr-con↗

arXiv2016

Correlation-enhanced odd-parity inter-orbital singlet pairing in the iron-pnictide superconductor LiFeAs

The rich variety of iron-based superconductors and their complex electronic structure lead to a wide range of possibilities for gap symmetry and pairing components. Here we solve in the 2-Fe Brillouin zone the full frequency-dependent linearized Eliashberg equations for LiFeAs with spin-fluctuation mediated pairing interactions. The magnetic excitations are calculated with the random phase approximation on a correlated electronic structure obtained with density functional theory and dynamical mean field theory. Correlations induce long-lived local moments with orbital-dependent dynamics. The interaction between electrons through Hund's coupling promotes inter-orbital magnetic susceptibility. As a consequence, the leading pairing channel, conventional $s^{+-}$, acquires sizeable inter-orbital $d_{xy}-d_{xz(yz)}$ singlet pairing with odd parity under glide-plane symmetry. These components reduce the superconducting gap magnitude induced by the intra-orbital components of the gap function at the electron pockets intersection where the Fe-d $t_{2g}$ orbitals strongly mix. This in turn makes the results consistent with available experiments on the angular dependence of the gaps observed on the different Fermi surfaces.

cond-mat.supr-con↗

arXiv2016

Mott transition and magnetism on the anisotropic triangular lattice

Spin-liquid behavior was recently suggested experimentally in the moderately one-dimensional organic compound $κ$-H$_3$(Cat-EDT-TTF)$_2$. This compound can be modeled by the one-band Hubbard model on the anisotropic triangular lattice with $t^\prime/t \simeq 1.5$, where $t'$ is the minority hopping. It thus becomes important to extend previous studies, that were performed in the range $0 \leq t'/t \leq 1.2$, to find out whether there is a regime where Mott insulating behavior can be found without long-range magnetic order. To this end, we study the above model in the range $1.2 \leq t'/t \leq 2$ using cluster dynamical mean-field theory (CDMFT). We argue that it is important to choose a symmetry-preserving cluster rather than a quasi one-dimensional cluster. We find that, upon increasing $t'/t$ beyond $t^\prime/t \approx 1.3$, the Mott transition at zero-temperature is replaced by a first-order transition separating a metallic state from a collinear magnetic insulating state. Nevertheless, at the physically relevant value $t^\prime/t \simeq 1.5$, the transitions toward the magnetic and the Mott insulating phases are very close. The phase diagram obtained in this study can provide a working basis for moderately one-dimensional compounds on the anisotropic triangular lattice.

cond-mat.str-el↗

arXiv2016

Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation

Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem. The maximum-entropy approach, based on bayesian inference, is the most widely used method to tackle that problem. Although the approach is well established and among the most reliable and efficient ones, useful developments of the method and of its implementation are still possible. In addition, while a few free software implementations are available, a well-documented, optimized, general purpose and user-friendly software dedicated to that specific task is still lacking. Here we analyze all aspects of the implementation that are critical for accuracy and speed, and present a highly optimized approach to maximum-entropy. Original algorithmic and conceptual contributions include (1) numerical approximations that yield a computational complexity that is almost independent of temperature and spectrum shape (including sharp Drude peaks in broad background for example) while ensuring quantitative accuracy of the result whenever precision of the data is sufficient, (2) a robust method of choosing the entropy weight $α$ that follows from a simple consistency condition of the approach and the observation that information- and noise-fitting regimes can be identified clearly from the behavior of $χ^2$ with respect to $α$, and (3) several diagnostics to assess the reliability of the result. Benchmarks with test spectral functions of different complexity and an example with an actual physical simulation are presented. Our implementation, which covers most typical cases for fermions, bosons and response functions, is available as an open source, user friendly software.

cond-mat.str-el↗

arXiv2016

Pseudogap and superconductivity in two-dimensional doped charge-transfer insulators

High-temperature superconductivity emerges in the CuO$_2$ plane upon doping a Mott insulator. To ascertain the influence of Mott physics plus short-range correlations, we solve a three-band copper-oxide model in the charge-transfer regime using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo as an impurity solver. We report the normal and superconducting phase diagram of this model as a function of doping, interaction strength and temperature. Upon hole doping of the charge-transfer insulator, the phase boundary between pseudogap and correlated metal consists of a first-order transition line at finite doping ending at a critical point, as in the one-band model. Beyond the endpoint, the phase boundary continues as a Widom crossover line, across which thermodynamic quantities peak. This phase boundary determines changes in the pairing mechanism and is an emergent phenomenon characteristic of doped Mott insulators, independent of many microscopic details. Broader implications are discussed.

cond-mat.str-el↗

arXiv2016

An organizing principle for two-dimensional strongly correlated superconductivity

Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature $T_c^d$, the maximum of the condensation energy as a function of doping, the correlation between maximum $T_c^d$ and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.

cond-mat.str-el↗

arXiv2015

Superconducting dome in doped quasi-2d organic Mott insulators: a paradigm for strongly-correlated superconductivity

Layered organic superconductors of the BEDT family are model systems for the interplay of the Mott transition with superconductivity, magnetic order and frustration. Recent experimental studies on a hole-doped version of BEDT compounds reveal an enhancement of superconductivity and a rapid crossover between two different conducting phases above the superconducting dome. One of these phases is a Fermi liquid, the other not. Using plaquette cellular dynamical mean field theory with state of the art continuous-time quantum Monte Carlo calculations, we study this problem with the two-dimensional Hubbard model on the anisotropic triangular lattice. Phase diagrams as a function of temperature $T$ and interaction strength $U/t$ are obtained for anisotropy parameters $t'=0.4t$, $t'=0.8t$ and various fillings. As for cuprates, we find, at finite doping, a first-order transition between two normal-state phases. For $T$ above the critical point of the first-order transition, there is a Widom line where crossovers occur. The results are in broad agreement with experiment. This suggests that for compounds with intermediate to high frustration, very light-doping should reveal the first-order transition and associated crossovers. These crossovers could leave traces in the superconducting phase. We also predict that destroying the superconducting phase by a magnetic field should reveal the first-order transition. Finally, we predict that electron-doping should also lead to an increased range of $U/t$ for superconductivity but with a reduced maximum $T_c$. This work also clearly shows that the superconducting dome here is tied to the Mott transition and its continuation as a transition separating pseudogap phase from correlated metal in doped compounds, as in the cuprates. Contrary to heavy fermions for example, the maximum $T_c$ is definitely not attached to an antiferromagnetic quantum critical point.

cond-mat.supr-con↗

arXiv2015

Maximum Entropy Analytic Continuation for Spectral Functions with Non-Positive Spectral Weight

Information about the pairing mechanism for superconductivity is contained in the spectral weight for the anomalous (Gorkov) Green function. In the most general case, this spectral weight can change sign on the positive real axis or even be complex in the presence of broken time-reversal symmetry. This renders impossible the direct analytic continuation with Maximum Entropy methods of numerical results obtained for the anomalous Green function either in Matsubara frequency or in imaginary time. Here we show that one can define auxiliary Green functions that allow one to extract the anomalous spectral weight in the most general multi-orbital spin-singlet or triplet cases with no particular symmetry. As a simple example, we treat the case of lead in Eliashberg theory: Maximum Entropy analytic continuation with auxiliary Green functions (MaxEntAux) allows us to recover spectral functions that change sign on the positive real axis. The approach can be extended to transport quantities.

cond-mat.supr-con↗

arXiv2015

Antiferromagnetism in the Hubbard model on the honeycomb lattice: a Two-Particle Self-Consistent study

The semimetal to antiferromagnet quantum phase transition of the Hubbard model on the honeycomb lattice has come to the forefront in the context of the proposal that a semimetal to spin liquid transition can occur before the transition to the antiferromagnetic phase. To study the semimetal to antiferromagnet transition, we generalize the two-particle self-consistent (TPSC) approach to the honeycomb lattice (a structure that can be realized in graphene for example). We show that the critical interaction strength where the transition occurs is $U_c/t=3.79\pm 0.01$ quite close to the value $U_c/t=3.869 \pm 0.013$ reported using large-scale quantum Monte Carlo simulations. This reinforces the conclusion that the semimetal to spin liquid transition is pre-empted by the transition to the antiferromagnet. Since TPSC satisfies the Mermin-Wagner theorem, we find temperature-dependent results for the antiferromagnetic and ferromagnetic correlation lengths as well as the dependence of double occupancy and of the renormalized spin and charge interactions on the bare interaction strength. We also estimate the value of the crossover temperature to the renormalized classical regime as a function of interaction strength.

cond-mat.str-el↗

arXiv2014

Electric polarization of Sr$_{0.5}$Ba$_{0.5}$MnO$_{3}$: a multiferroic Mott insulator

Ab initio calculations of the electric polarization of correlation-driven insulating materials, namely Mott insulators, have not been possible so far. Using a combination of density functional theory and dynamical-mean-field theory we study the electric polarization of the Mott insulator Sr$_{0.5}$Ba$_{0.5}$MnO$_{3}$. We predict a ferroelectric polarization of $\simeq 16.5 μC/cm^2$ in the high temperature paramagnetic phase and recover the measured value of $\simeq 13.3 μC/cm^2$ in the low temperature antiferromagnetic phase. Our calculations reveal that the driving force for the ferroelectricity, the hybridization between Mn e$_g$ and O p orbitals, is suppressed by correlations, in particular by the Hund coupling and by the onset of magnetic order. They also confirm that the half-filled Mn $t_{2g}$ orbitals give rise to the antiferromagnetic Mott phase. This magnetic ordering leads to changes in the ionic polar displacement and in turn to the electronic polarization. In addition, for a fixed ionic displacement, we find that there is a reduction in the electronic contribution due to partial magnetic polarization of the Mn e$_g$ orbitals. The reduction of the polarization due to ionic displacement dominates over the additional electronic part, hence the net magneto-electric coupling is negative.

cond-mat.mtrl-sci↗

arXiv2014

Impurity-induced magnetic moments on the graphene-lattice Hubbard model: an inhomogeneous cluster DMFT study

Defect-induced magnetic moments are at the center of the research effort on spintronic applications of graphene. Here we study the problem of a nonmagnetic impurity in graphene with a new theoretical method, inhomogeneous cluster dynamical mean field theory (I-CDMFT), which takes into account interaction-induced short-range correlations while allowing long-range inhomogeneities. The system is described by a Hubbard model on the honeycomb lattice. The impurity is modeled by a local potential. For a large enough potential, interactions induce local antiferromagnetic correlations around the impurity and a net total spin $\frac12$ appears, in agreement with Lieb's theorem. Bound states caused by the impurity are visible in the local density of states (LDOS) and have their energies shifted by interactions in a spin-dependent way, leading to the antiferromagnetic correlations. Our results take into account dynamical correlations; nevertheless they qualitatively agree with previous mean-field and density functional theory (DFT) studies. Moreover, they provide a relation between impurity potential and on-site repulsion $U$ that could in principle be used to determine experimentally the value of $U$.

cond-mat.str-el↗

arXiv2014

Lazy skip lists, a new algorithm for fast hybridization-expansion quantum Monte Carlo

The solution of a generalized impurity model lies at the heart of electronic structure calculations with dynamical mean-field theory (DMFT). In the strongly-correlated regime, the method of choice for solving the impurity model is the hybridization expansion continuous time quantum Monte Carlo(CT-HYB). Enhancements to the CT-HYB algorithm are critical for bringing new physical regimes within reach of current computational power. Taking advantage of the fact that the bottleneck in the algorithm is a product of hundreds of matrices, we present optimizations based on the introduction and combination of two concepts of more general applicability: a) skip lists and b) fast rejection of proposed configurations based on matrix bounds. Considering two very different test cases with $d$ electrons, we find speedups of $\sim 25$ up to $\sim 500$ compared to the direct evaluation of the matrix product. Even larger speedups are likely with $f$ electron systems and with clusters of correlated atoms.

cond-mat.str-el↗

arXiv2014

Orbital magnetization of correlated electrons with arbitrary band topology

Spin-orbit coupling introduces chirality into electronic structure. This can have profound effects on the magnetization induced by orbital motion of electrons. Here we derive a formula for the orbital magnetization of interacting electrons in terms of the full Green's function and vertex functions. The formula is applied within dynamical mean-field theory to the Kane-Mele-Hubbard model that allows both topological and trivial insulating phases. We study the insulating and metallic phases in the presence of an exchange magnetic field. In the presence of interactions, the orbital magnetization of the quantum spin Hall insulating phase with inversion symmetry is renormalized by the bulk quasi-particle weight. The orbital magnetization vanishes for the in-plane antiferromagnetic phase with trivial topology. In the metallic phase, the enhanced effective spin-orbit coupling due to the interaction sometimes leads to an enhancement of the orbital magnetization. However, at low doping, magnetization is suppressed at large interaction strengths.

cond-mat.str-el↗

arXiv2014

Ergodicity of the Hybridization-Expansion Monte Carlo Algorithm for Broken-Symmetry States

With the success of dynamical mean field theories, solvers for quantum-impurity problems have become an important tool for the numerical study of strongly correlated systems. Continuous-time Quantum Monte Carlo sampling of the expansion in powers of the hybridization between the ``impurity'' and the bath provides a powerful solver when interactions are strong. Here we show that the usual updates that add or remove a pair of creation-annihilation operators are rigorously not ergodic for several classes of broken-symmetries that involve spatial components. We show that updates with larger numbers of simultaneous updates of pairs of creation-annihilation operators remedy this problem. As an example, we apply the four operator updates that are necessary for ergodicity to the case of d-wave superconductivity in plaquette dynamical mean-field theory for the one-band Hubbard model. While the results are qualitatively similar to those previously published, they are quantitatively better that previous ones, being closer to those obtained by other approaches.

cond-mat.str-el↗

arXiv2013

Transport functions for hypercubic and Bethe lattices

In calculations of transport quantities, such as the electrical conductivity, thermal conductivity, Seebeck, Peltier, Nernst, Ettingshausen, Righi-Leduc, or Hall coefficients, sums over the Brillouin zone of wave-vector derivatives of the dispersion relation commonly appear. When the self-energy depends only on frequency, as in single-site dynamical mean-field theory, it is advantageous to perform these sums once and for all. We show here that in the case of a hypercubic lattice in d dimensions, the sums needed for any of the transport coefficients can be expressed as integrals over powers of the energy weighted by the energy-dependent non-interacting density of states. It is also shown that our exact expressions for the transport functions can be obtained from differential equations that follow from sum rules. By substituting the Bethe lattice density of states, one can obtain the previously unknown transport function for the electrical or thermal Hall coefficients and for the Nernst coefficient of the Bethe lattice.

cond-mat.str-el↗

arXiv2013

Strongly correlated superconductivity

Band theory and BCS theory are arguably the most successful theories of condensed matter physics. Yet, in a number of materials, in particular the high-temperature superconductors and the layered organic superconductors, they fail. In these lecture notes for an international school, I emphasize that even though the low energy properties of a phase of matter are generally emergent and entirely determined by the broken symmetry, there are many differences between a strongly correlated and a weakly correlated state of matter. For example, spin waves are an emergent property for antiferromagnets, but for weak correlations the normal phase of a (Slater) antiferromagnet is metallic, whereas it is insulating (Heisenberg) for strong correlations. As a function of interaction strength, above the antiferromagnetic phase, the crossover between a metal and a local moment paramagnetic insulator is described by the Mott transition, whose mean-field theory down to T=0 is best formulated with dynamical mean-field theory. A similar situation occurs for superconductors: despite similar emergent properties, there are many differences between both kinds of superconductors. Experimental evidence suggests that hole-doped cuprates are strongly correlated whereas the correlations are weaker in the electron-doped case, especially near optimal doping. Evidence for a pseudogap arising from antiferromagnetic fluctuations is strong in the latter case, whereas in the hole-doped case the pseudogap temperature appears as a consequence of Mott physics. In cluster dynamical mean-field theory, the pseudogap line T* is a Widom line arising from a T=0 first-order transition that terminates at a finite T critical point. Strongly correlated superconductors are much more resilient to near-neighbor repulsion than their weakly correlated counterpart. Many different methods to attack these problems theoretically are described.

cond-mat.supr-con↗