Density matrix embedding: A simple alternative to dynamical mean-field theory

TL;DR

DMET is a new quantum embedding method that simplifies the modeling of infinite systems by using a frequency-independent local density matrix and a minimal bath, achieving high accuracy with low computational cost.

Contribution

DMET introduces a novel, efficient quantum embedding approach based on the local density matrix, differing from DMFT by avoiding Green's functions and discretization errors.

Findings

Accurately predicts ground-state properties of Hubbard models

Reproduces total energies and correlation functions well

Identifies metal-insulator transitions with high fidelity

Abstract

We introduce DMET, a new quantum embedding theory for predicting ground-state properties of infinite systems. Like dynamical mean-field theory (DMFT), DMET maps the the bulk interacting system to a simpler impurity model and is exact in the non-interacting and atomic limits. Unlike DMFT, DMET is formulated in terms of the frequency-independent local density matrix, rather than the local Green's function. In addition, it features a finite, algebraically constructible bath of only one bath site per impurity site, which exactly embeds ground-states at a mean-field level with no bath discretization error. Frequency independence and the minimal bath make DMET a computationally simple and very efficient method. We test the theory in the 1D and 2D Hubbard models at and away from half-filling, and we find that compared to benchmark data, total energies, correlation functions, and paramagnetic metal-insulator transitions are well reproduced, at a tiny computational cost.