Finite Size Scaling for Low Energy Excitations in Integer Heisenberg Spin Chains

TL;DR

This study investigates the finite size scaling of low energy excitations in integer Heisenberg spin chains using DMRG, revealing crossover behaviors and edge state phenomena in chains of different lengths and spins.

Contribution

It provides new insights into the finite size scaling behavior and edge state properties of S=1 and S=2 Heisenberg chains, including crossover from 1/L to 1/L^2 scaling.

Findings

Crossover from 1/L to 1/L^2 scaling in excitations with chain length

Identification of topological S=1/2 edge states in open and periodic chains

Quantitative values for gap and correlation length in S=2 chains

Abstract

In this paper we study the finite size scaling for low energy excitations of $S=1$ and $S=2$ Heisenberg chains, using the density matrix renormalization group technique. A crossover from $1/L$ behavior (with $L$ as the chain length) for medium chain length to $1/L^2$ scaling for long chain length is found for excitations in the continuum band as the length of the open chain increases. Topological spin $S=1/2$ excitations are shown to give rise to the two lowest energy states for both open and periodic $S=1$ chains. In periodic chains these two excitations are ``confined'' next to each other, while for open chains they are two free edge 1/2 spins. The finite size scaling of the two lowest energy excitations of open $S=2$ chains is determined by coupling the two free edge $S=1$ spins. The gap and correlation length for $S=2$ open Heisenberg chains are shown to be 0.082 (in units of the exchange $J$) and 47, respectively.