Luttinger liquid behavior in spin chains with a magnetic field

TL;DR

This paper numerically investigates the Luttinger liquid behavior in antiferromagnetic Heisenberg spin chains under strong magnetic fields, focusing on the dressed charge and critical parameters for S=1/2 and S=1 chains.

Contribution

It provides precise numerical estimates of the Luttinger liquid dressed charge and other parameters for different spin chains using DMRG, highlighting differences between S=1/2 and S=1 systems.

Findings

Dressed charge Z varies with magnetization in both chains.

Critical amplitudes and scattering lengths are quantified.

Parameters differ significantly between S=1/2 and S=1 chains.

Abstract

Antiferromagnetic Heisenberg spin chains in a sufficiently strong magnetic field are Luttinger liquids, whose parameters depend on the actual magnetization of the chain. Here we present precise numerical estimates of the Luttinger liquid dressed charge $Z$, which determines the critical exponents, by calculating the magnetization and quadrupole operator profiles for $S=1/2$ and S=1 chains using the density matrix renormalization group method. Critical amplitudes and the scattering length at the chain ends are also determined. Although both systems are Luttinger liquids the characteristic parameters differ considerably.