Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory

Gerald Knizia and Garnet Kin-Lic Chan
Phys. Rev. Lett. 109, 186404 – Published 2 November 2012

Abstract

We introduce density matrix embedding theory (DMET), a quantum embedding theory for computing frequency-independent quantities, such as ground-state properties, of infinite systems. Like dynamical mean-field theory, DMET maps the bulk interacting system to a simpler impurity model and is exact in the noninteracting and atomic limits. Unlike dynamical mean-field theory, 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, with no bath discretization error. Frequency independence and the minimal bath make DMET a computationally simple and efficient method. We test the theory in the one-dimensional and two-dimensional Hubbard models at and away from half filling, and we find that compared to benchmark data, total energies, correlation functions, and metal-insulator transitions are well reproduced, at a tiny computational cost.

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  • Received 25 April 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.186404

© 2012 American Physical Society

Authors & Affiliations

Gerald Knizia and Garnet Kin-Lic Chan

  • Department of Chemistry, Frick Laboratory, Princeton University, Princeton, New Jersey 08544, USA

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Issue

Vol. 109, Iss. 18 — 2 November 2012

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