Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory
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.
© 2012 American Physical Society. Received 25 April 2012; published 2 November 2012. Support was provided from the U.S. Department of Energy, Office of Science, through Grant No. DE-FG02-07ER46432, and the Computational Materials Science Network (DE-SC0006613). We acknowledge helpful discussions with A. Millis, D. Reichman, and C. Marianetti.
Accepted Version - 1204.5783.pdf
Published - PhysRevLett.109.186404.pdf