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The density matrix renormalization group (DMRG) method allows an efficientcomputation of the properties of interacting 1D quantum systems.Two-dimensional (2D) systems, capable of displaying much richer quantumbehavior, 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, forwhich, unfortunately, the standard 2D DMRG algorithm fares little better. Byfinding the form of the entanglement entropy in quasi-1D systems, we directlyidentify the reason for this failure. Using this understanding, we explain whya modified algorithm, capable of cleverly exploiting this behavior of theentanglement entropy, can accurately reach much larger system sizes. Wedemonstrate the power of this method by accurately finding quantum criticalpoints in frustration induced magnetic transitions, which remain inaccessibleusing the standard DMRG or the Monte Carlo methods.

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