Finite temperature density matrix embedding theory

TL;DR

This paper extends density matrix embedding theory to finite temperatures, demonstrating its effectiveness on Hubbard models and showing comparable accuracy to existing methods with modest computational cost.

Contribution

It introduces a finite-temperature formulation of density matrix embedding theory with a generalized bath construction method.

Findings

Accurately models Hubbard systems at finite temperature.

Performance comparable to cluster dynamical mean-field theory.

Requires only a modest increase in bath size.

Abstract

We describe a formulation of the density matrix embedding theory at finite temperature. We present a generalization of the ground-state bath orbital construction that embeds a mean-field finite-temperature density matrix up to a given order in the Hamiltonian, or the Hamiltonian up to a given order in the density matrix. We assess the performance of the finite-temperature density matrix embedding on the 1D Hubbard model both at half-filling and away from it, and the 2D Hubbard model at half-filling, comparing to exact data where available, as well as results from finite-temperature density matrix renormalization group, dynamical mean-field theory, and dynamical cluster approximations. The accuracy of finite-temperature density matrix embedding appears comparable to that of the ground-state theory, with at most a modest increase in bath size, and competitive with that of cluster dynamical mean-field theory.