Tomonaga-Luttinger-liquid criticality: numerical entanglement entropy approach

Abstract

The von Neumann entanglement entropy is studied with the density-matrix renormalization group technique. We propose a simple approach to calculate the central charge using the entanglement entropy for one-dimensional (1D) quantum system. This approach is applied to a couple of quantum systems: (i) 1D frustrated spin model and (ii) 1D half-filled spinless fermions with nearest-neighbor repulsion; and, it is confirmed that the central charge is estimated very accurately for the both systems. Also, a new method to determine the critical point between TL-liquid and gapped (or ordered) phases from the proposed approach is suggested. Furthermore, we mention that the Tomonaga-Luttinger parameter can be obtained in a like manner as the central charge, using the charge-density fluctuation of a part of the 1D system.