Accessing thermodynamics from dynamical cluster-embedding approaches

TL;DR

This paper introduces an efficient numerical algorithm to compute the thermodynamic grand potential within dynamical cluster-embedding approaches, enabling access to thermodynamics in strongly correlated electron systems using continuous-time QMC methods.

Contribution

The authors develop a novel quantum Wang-Landau reweighting technique to accurately calculate the grand potential in cluster DMFT and VCA frameworks, bridging a gap in thermodynamic analysis.

Findings

Successfully applied to the 2D Hubbard model at finite temperature.

Demonstrates the method's ability to handle antiferromagnetic order.

Provides a controlled way to access thermodynamics in cluster approaches.

Abstract

Dynamical quantum-cluster approaches, such as different cluster extensions of the dynamical mean-field theory (cluster DMFT) or the variational cluster approximation (VCA), combined with efficient cluster solvers, such as the quantum Monte-Carlo (QMC) method, provide controlled approximations of the single-particle Green's function for lattice models of strongly correlated electrons. To access the thermodynamics, however, a thermodynamical potential is needed. We present an efficient numerical algorithm to compute the grand potential within cluster-embedding approaches that are based on novel continuous-time QMC schemes: It is shown that the numerically exact cluster grand potential can be obtained from a quantum Wang-Landau technique to reweight the coefficients in the expansion of the partition function. The lattice contributions to the grand potential are computed by a proper infinite summation over Matsubara frequencies. A proof of principle is given by applying the VCA to antiferromagnetic (short-range) order in the two-dimensional Hubbard model at finite temperatures.