Response of finite spin-S Heisenberg chains to local perturbations

TL;DR

This study investigates how finite antiferromagnetic Heisenberg chains with various spin values respond to local magnetic perturbations, revealing distinct correlation behaviors and boundary effects using DMRG methods.

Contribution

It provides a detailed analysis of local perturbation effects on finite spin chains with different S values, highlighting unique boundary and correlation properties.

Findings

For S=1, a single length scale governs correlation functions.

Critical half-odd-integer spins exhibit a correlation exponent η=1.

Behavior near free boundaries differs significantly between S=1/2 and S>1/2.

Abstract

We consider the properties of finite isotropic antiferromagnetic Heisenberg chains with S=1/2, 1, 3/2 spins when a weak magnetic field is applied on a few sites, using White's density matrix renormalization group (DMRG) method. For the S=1 chain there exists only one length scale in the system which determines the behavior of the one- and two-point correlation functions both around the local perturbation and near the free boundary. For the critical, half-odd-integer spin cases the exponent of the spin-spin correlation function was found to be $\eta=1$, and the exponent of the decay of the site magnetization around the perturbed site is $x_m =\eta /2 $. Close to a free boundary, however, the behavior is completely different for S=1/2 and $S > 1/2$.