Edge Spin fractionalization in one-dimensional spin-$S$ quantum antiferromagnets

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Kattel, Pradip, Tang, Yicheng, Pixley, J. H., Andrei, Natan
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909635391258624
author Kattel, Pradip
Tang, Yicheng
Pixley, J. H.
Andrei, Natan
author_facet Kattel, Pradip
Tang, Yicheng
Pixley, J. H.
Andrei, Natan
contents We show that a gapped spin-$S$ chain with antiferromagnetic (AFM) order exhibits in the thermodynamic limit exponentially localized fractional $\pm \frac{S}{2}$ edge modes when the system possesses U(1) symmetry. We show this for integrable and non integrable spin chains both analytically and numerically. Through exact analytical solutions, we show that an AFM spin-$\frac{1}{2}$ chain with {\it explicitly} broken $\mathbb{Z}_2$ symmetry and an integrable AFM spin-$1$ chain with {\it spontaneously} broken $\mathbb{Z}_2$ symmetry have $\pm \frac{1}{4}$ and $\pm \frac{1}{2}$ fractionalized edge modes, respectively. Furthermore, employing the density matrix renormalization group technique, we extend this analysis to {\it generic} $XXZ-S$ chains with $S\leq 3$ and demonstrate that these fractional spins are robust quantum observables, substantiated by the observation of a variance of the associated fractional spin operators that is consistent with a vanishing functional form in the thermodynamic limit. Moreover, we find that the edge modes are robust to disorder that couples to the Néel order parameter.
format Preprint
id arxiv_https___arxiv_org_abs_2406_11955
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Edge Spin fractionalization in one-dimensional spin-$S$ quantum antiferromagnets
Kattel, Pradip
Tang, Yicheng
Pixley, J. H.
Andrei, Natan
Strongly Correlated Electrons
Statistical Mechanics
Mathematical Physics
We show that a gapped spin-$S$ chain with antiferromagnetic (AFM) order exhibits in the thermodynamic limit exponentially localized fractional $\pm \frac{S}{2}$ edge modes when the system possesses U(1) symmetry. We show this for integrable and non integrable spin chains both analytically and numerically. Through exact analytical solutions, we show that an AFM spin-$\frac{1}{2}$ chain with {\it explicitly} broken $\mathbb{Z}_2$ symmetry and an integrable AFM spin-$1$ chain with {\it spontaneously} broken $\mathbb{Z}_2$ symmetry have $\pm \frac{1}{4}$ and $\pm \frac{1}{2}$ fractionalized edge modes, respectively. Furthermore, employing the density matrix renormalization group technique, we extend this analysis to {\it generic} $XXZ-S$ chains with $S\leq 3$ and demonstrate that these fractional spins are robust quantum observables, substantiated by the observation of a variance of the associated fractional spin operators that is consistent with a vanishing functional form in the thermodynamic limit. Moreover, we find that the edge modes are robust to disorder that couples to the Néel order parameter.
title Edge Spin fractionalization in one-dimensional spin-$S$ quantum antiferromagnets
topic Strongly Correlated Electrons
Statistical Mechanics
Mathematical Physics
url https://arxiv.org/abs/2406.11955