The behavior of the entanglement entropy in interacting quasi-1D systems and its consequences for their efficient numerical study

Abstract

The density matrix renormalization group (DMRG) method allows an efficient computation of the properties of interacting 1D quantum systems. Two-dimensional (2D) systems, capable of displaying much richer quantum behavior, generally lie beyond its reach except for very small system sizes. Many of the physical properties of 2D systems carry into the quasi-1D case, for which, unfortunately, the standard 2D DMRG algorithm fares little better. By finding the form of the entanglement entropy in quasi-1D systems, we directly identify the reason for this failure. Using this understanding, we explain why a modified algorithm, capable of cleverly exploiting this behavior of the entanglement entropy, can accurately reach much larger system sizes. We demonstrate the power of this method by accurately finding quantum critical points in frustration induced magnetic transitions, which remain inaccessible using the standard DMRG or the Monte Carlo methods.