Random SU(2)-symmetric spin-$S$ chains

TL;DR

This paper investigates the low-energy behavior of disordered SU(2)-symmetric spin chains, revealing emergent symmetries, distinct random singlet phases, and various phases with activated or power-law dynamics.

Contribution

It introduces a comprehensive analysis of disordered spin-$S$ chains, uncovering emergent SU(2S+1) symmetry and characterizing multiple phases with unique ground states and dynamical properties.

Findings

Emergent SU(2S+1) symmetry in antiferromagnetic phase

Distinct random singlet states for integer and half-integer spins

Identification of phases with activated and power-law dynamics

Abstract

We study the low-energy physics of a broad class of time-reversal invariant and SU(2)-symmetric one-dimensional spin-S systems in the presence of quenched disorder via a strong-disorder renormalization-group technique. We show that, in general, there is an antiferromagnetic phase with an emergent SU(2S+1) symmetry. The ground state of this phase is a random singlet state in which the singlets are formed by pairs of spins. For integer spins, there is an additional antiferromagnetic phase which does not exhibit any emergent symmetry (except for S=1). The corresponding ground state is a random singlet one but the singlets are formed mostly by trios of spins. In each case the corresponding low-energy dynamics is activated, i.e., with a formally infinite dynamical exponent, and related to distinct infinite-randomness fixed points. The phase diagram has two other phases with ferromagnetic tendencies: a disordered ferromagnetic phase and a large spin phase in which the effective disorder is asymptotically finite. In the latter case, the dynamical scaling is governed by a conventional power law with a finite dynamical exponent.