Studying Two Dimensional Systems With the Density Matrix Renormalization Group

Abstract

The Density Matrix Renormalization Group (DMRG) method scales exponentially in the system width for models in two dimensions, but remains one of the most powerful methods for studying 2D systems with a sign problem. Reviewing past applications of DMRG in 2D demonstrates its success in treating a wide variety of problems, although it remains underutilized in this setting. We present techniques for performing cutting edge 2D DMRG studies including methods for ensuring convergence, extrapolating finite-size data and extracting gaps and excited states. Finally, we compare the current performance of a recently developed tensor network method to 2D DMRG.

Expanded introduction, added references and other minor changes throughout. 11 pages, 9 figures, To appear in Annual Reviews of Condensed Matter Physics (2012) [without the abstract]

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