arXiv subjects

Emanuel Gull

Publications and source records attributed to Emanuel Gull.

At least 109 records · Page 6Linked to original sources

arXiv2016

Charge ordering and correlation effects in the extended Hubbard model

We study the half filled extended Hubbard model on a two-dimensional square lattice using cluster dynamical mean field theory on clusters of size 8-20. We show that the model exhibits metallic, Mott insulating, and charge ordered phases, and determine the location of the charge ordering phase transition line and the properties of the ordered and disordered phase as a function of temperature, local interaction, and nearest neighbor interaction. We find strong non-local correlations in the uniform phase and a pronounced screening effect in the vicinity of the phase transition, where non-local interactions push the system towards metallic behavior. In contrast, correlations in the ordered phase are mostly local to the unit cell. Extrapolation to the thermodynamic limit and control of all sources of errors allow us to assess the regime of applicability of simpler approximation schemes for systems with non-local interactions. We also demonstrate how strong non-local electron-electron interactions can increase electron mobility by turning a charge ordered insulator into a metal.

cond-mat.str-el↗

arXiv2016

Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo

We generalize the recently developed inchworm quantum Monte Carlo method to the full Keldysh contour with forward, backward, and equilibrium branches to describe the dynamics of strongly correlated impurity problems with time dependent parameters. We introduce a method to compute Green's functions, spectral functions, and currents for inchworm Monte Carlo and show how systematic error assessments in real time can be obtained. We then illustrate the capabilities of the algorithm with a study of the behavior of quantum impurities after an instantaneous voltage quench from a thermal equilibrium state.

cond-mat.str-el↗

arXiv2016

Knight shifts, nuclear spin-relaxation rates, and spin echo decay times in the pseudogap regime of the cuprates: Simulation and relation to experiment

We study the temperature and doping evolution of the NMR Knight shift, spin relaxation rate, and spin echo decay time in the pseudogap regime of the two-dimensional Hubbard model for parameters believed to be relevant to cuprate superconductors using cluster dynamical mean field theory. We recover the suppression of the Knight shift seen in experiment upon entering the pseudogap regime and find agreement between single and two-particle measures of the pseudogap onset temperature. The simulated spin-echo decay time shows a linear in T behavior at high T which flattens off as T is lowered, and increases as doping is increased. The relaxation rate shows a marked increase as T is lowered but no indication of a pseudogap on the Cu site, and a clear downturn on the O site, consistent with experimental results on single layer materials but different from double layer materials. The consistency of the simulated susceptibilities with experiment, along with similar agreement on the single-particle level and the absence of long-range order and symmetry breaking suggests that the pseudogap is well described by strong short-range correlation effects and that long-range order and multi-orbital effects are not required.

cond-mat.str-el↗

arXiv2016

Diagrammatic Monte Carlo for Dual Fermions

We introduce a numerical algorithm to stochastically sample the dual fermion perturbation series around the dynamical mean field theory, generating all topologies of two-particle interaction vertices. We show results in the weak and strong coupling regime of the half-filled Hubbard model in two dimensions, illustrating that the method converges quickly where dynamical mean field theory is a good approximation, and show that corrections are large in the strong correlation regime at intermediate interaction. The fast convergence of dual corrections to dynamical mean field results illustrates the power of the approach and opens a practical avenue towards the systematic inclusion of non-local correlations in correlated materials simulations. An analysis of the frequency scale shows that only low-frequency propagators contribute substantially to the diagrams, putting the inclusion of higher order vertices within reach.

cond-mat.str-el↗

arXiv2016

Implementation of the Maximum Entropy Method for Analytic Continuation

We present $\texttt{Maxent}$, a tool for performing analytic continuation of spectral functions using the maximum entropy method. The code operates on discrete imaginary axis datasets (values with uncertainties) and transforms this input to the real axis. The code works for imaginary time and Matsubara frequency data and implements the 'Legendre' representation of finite temperature Green's functions. It implements a variety of kernels, default models, and grids for continuing bosonic, fermionic, anomalous, and other data. Our implementation is licensed under GPLv2 and extensively documented. This paper shows the use of the programs in detail.

physics.comp-ph↗

arXiv2016

Efficient temperature-dependent Green's function methods for realistic systems: using cubic spline interpolation to approximate Matsubara Green's functions

The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about two orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one- and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be doubled, whereas for the Matsubara frequency grid an order of magnitude more grid points must be used. This suggests that realistic calculations with large basis sets that were previously out of reach because they required enormous grid sizes may now become feasible.

physics.chem-ph↗

arXiv2015

Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

cond-mat.str-el↗

arXiv2015

Mechanisms of finite temperature magnetism in the three-dimensional Hubbard model

We examine the nature of the transition to the antiferromagnetically ordered state in the half-filled three-dimensional Hubbard model using the dual-fermion multiscale approach. Consistent with analytics, in the weak-coupling regime we find that spin-flip excitations across the Fermi surface are important, and that the strong coupling regime is described by Heisenberg physics. In the intermediate interaction, strong correlation regime we find aspects of both local and non-local correlations. We analyze the critical exponents of the transition in the strong coupling regime and find them to be consistent with Heisenberg physics down to an interaction of $U/t=10$.

cond-mat.str-el↗

arXiv2015

Taming the dynamical sign problem in real-time evolution of quantum many-body problems

Current nonequilibrium Monte Carlo methods suffer from a dynamical sign problem that makes simulating real-time dynamics for long times exponentially hard. We propose a new `Inchworm Algorithm', based on iteratively reusing information obtained in previous steps to extend the propagation to longer times. The algorithm largely overcomes the dynamical sign problem, changing the scaling from exponential to quadratic. We use the method to solve the Anderson impurity model in the Kondo and mixed valence regimes, obtaining results both for quenches and for spin dynamics in the presence of an oscillatory magnetic field.

cond-mat.str-el↗

arXiv2015

Thermodynamics of the Hubbard model on stacked honeycomb and square lattices

We present a numerical study of the Hubbard model on simply stacked honeycomb and square lattices, motivated by a recent experimental realization of such models with ultracold atoms in optical lattices. We perform simulations with different interlayer coupling and interaction strengths and obtain Néel transition temperatures and entropies. We provide data for the equation of state to enable comparisons of experiments and theory. We find an enhancement of the short-range correlations in the anisotropic lattices compared to the isotropic cubic lattice, in parameter regimes suitable for the interaction driven adiabatic cooling.

cond-mat.quant-gas↗

arXiv2015

Continuous-time Quantum Monte Carlo using Worm Sampling

We present a worm sampling method for calculating one- and two-particle Green's functions using continuous-time quantum Monte Carlo simulations in the hybridization expansion (CT-HYB). Instead of measuring Green's functions by removing hybridization lines from partition function configurations, as in conventional CT-HYB, the worm algorithm directly samples the Green's function. We show that worm sampling is necessary to obtain general two-particle Green's functions which are not of density-density type and that it improves the sampling efficiency when approaching the atomic limit. Such two-particle Green's functions are needed to compute off-diagonal elements of susceptibilities and occur in diagrammatic extensions of the dynamical mean field theory and efficient estimators for the single-particle self-energy.

cond-mat.str-el↗

arXiv2015

Superconducting Fluctuations in the Normal State of the Two-Dimensional Hubbard Model

We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the $d_{x^2-y^2}$ superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half-filling. We find a change in sign of the vertex contributions to $d_{xy}$ superconductivity from repulsive near half filling to attractive at large doping. $p$-wave superconductivity is not found at the parameters we study, and $s$-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase $T_c$.

cond-mat.supr-con↗

arXiv2015

Voltage quench dynamics of a Kondo system

We examine the dynamics of a correlated quantum dot in the mixed valence regime. We perform numerically exact calculations of the current after a quantum quench from equilibrium by rapidly applying a bias voltage in a wide range of initial temperatures. The current exhibits short equilibration times and saturates upon the decrease of temperature at all times, indicating Kondo behavior both in the transient regime and in steady state. The time-dependent current saturation temperature matches the Kondo temperature at small times or small voltages; a substantially increased value is observed outside of linear response. These signatures are directly observable by experiments in the time-domain.

cond-mat.str-el↗

arXiv2015

opendf - an implementation of the dual fermion method for strongly correlated systems

The dual fermion method is a multiscale approach for solving lattice problems of interacting strongly correlated systems. In this paper, we present the \texttt{opendf} code, an open-source implementation of the dual fermion method applicable to fermionic single-orbital lattice models in dimensions $D=1,2,3$ and $4$. The method is built on a dynamical mean field starting point, which neglects all local correlations, and perturbatively adds spatial correlations. Our code is distributed as an open-source package under the GNU public license version 2.

cond-mat.str-el↗

arXiv2015

Systematically improvable multi-scale solver for correlated electron systems

The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between self-consistent second order perturbation theory and exact diagonalization can be used as a multi-scale solver for such systems. Using a quantum impurity model, generated from a cluster dynamical mean field approximation to the 2D Hubbard model, as a benchmark, we show that our method allows us to obtain accurate results at a fraction of the cost of typical Monte Carlo calculations. We test the behavior of our method in multiple regimes of interaction strengths and doping of the model. The algorithm avoids difficulties such as double counting corrections, frequency dependent interactions, or vertex functions. As it is solely formulated at the level of the single-particle Green's function, it provides a promising route for the simulation of realistic materials that are currently difficult to study with other methods.

cond-mat.str-el↗

arXiv2015

Quasiparticle Properties of the Superconducting State of the Two Dimensional Hubbard Model

Cluster dynamical mean field methods are used to calculate the normal and anomalous components of the electron self energy of the two dimensional Hubbard model. From these the evolution of the superconducting gap and the momentum dependent photoemission and inverse photoemission spectra across the phase diagram are determined. In the pseudogap regime, decreasing the temperature into the superconducting state leads to a decrease in the energy gap and the formation of a `peak-dip-hump' structure in the electronic density of states. The peak feature disperses very weakly. The calculated spectral functions are in good qualitative agreement with published data. The mathematical origin of the behavior is found to be the effect of the superconductivity on the pole structure giving rise to the normal state pseudogap. In particular the "hump" feature is found to arise from a zero crossing of the real part of the electron self energy rather than from an onset of scattering. The effect of superconductivity on the zone diagonal spectra is presented.

cond-mat.str-el↗

arXiv2014

Pairing Glue in the Two Dimensional Hubbard Model

Cluster dynamical mean field calculations are used to construct the superconducting gap function of the two dimensional Hubbard model. The frequency dependence of the imaginary part of the gap function indicates that the pairing is dominated by fluctuations at two characteristic frequencies: one at the scale of the hopping matrix element $t$ and one at a much lower scale. The lower frequency component becomes more important as the doping is reduced into the pseudogap regime. Comparison to available information on the spin fluctuation spectrum of the model suggests that the superconductivity arises from exchange of spin fluctuations. The inferred pairing glue function is in remarkable qualitative consistency with the pairing function inferred from time-resolved optical conductivity data.

cond-mat.str-el↗

arXiv2014

Critical Exponents of Strongly Correlated Fermion Systems from Diagrammatic Multi-Scale Methods

Self-consistent dynamical approximations for strongly correlated fermion systems are particularly successful in capturing the dynamical competition of local correlations. In these, the effect of spatially extended degrees of freedom is usually only taken into account in a mean field fashion or as a secondary effect. As a result, critical exponents associated with phase transitions have mean field character. Here, we demonstrate that diagrammatic multi-scale methods anchored around local approximations are indeed capable of capturing the non mean-field nature of the critical point of the lattice model encoded in a non-vanishing anomalous dimension, and to correctly describe the transition to mean field like behavior as the number of spatial dimensions increases.

cond-mat.str-el↗