Entanglement Entropy, Conformal Invariance and the Critical Behavior of the Anisotropic Spin-S Heisenberg Chains: A DMRG study

TL;DR

This study uses DMRG to analyze the critical behavior of anisotropic spin-$S$ Heisenberg chains, leveraging conformal invariance to accurately estimate key parameters without fitting.

Contribution

It introduces a method to precisely determine conformal and surface exponents of spin-$S$ chains using DMRG and conformal invariance, for spins up to 9/2.

Findings

Entanglement entropy difference follows a simple relation for S>3/2.

Accurate estimates of conformal anomaly, sound velocity, and exponents obtained.

Method avoids fitting parameters, enhancing precision.

Abstract

Using the density-matrix renormalization-group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to $S=9/2$. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly $c$, the sound velocity $v_{s}$, the anomalous dimension $x_{bulk}$, and the surface exponent $x_{s}$ of the anisotropic spin-$S$ Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entrop $S(L,l_{A},S)$ of the spin-$S$ Heisenberg chains satisfies the relation $S(L,l_{A},S)-S(L,l_{A},S-1)=1/(2S+1)$ for $S>3/2$ in the thermodynamic limit.