Tomonaga-Luttinger-liquid criticality: numerical entanglement entropy approach

TL;DR

This paper introduces a straightforward entanglement entropy-based method to accurately determine the central charge and critical points in 1D quantum systems, demonstrated on spin and fermion models.

Contribution

A novel, simple approach using entanglement entropy to estimate the central charge and critical points in 1D quantum systems.

Findings

Accurate estimation of central charge in spin and fermion models

Effective determination of phase transition points

Method to extract Tomonaga-Luttinger parameter from charge fluctuations

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.