Resilience of hidden order to symmetry-preserving disorder

TL;DR

This paper investigates how non-local string order in disordered spin chains remains robust despite symmetry-preserving disorder, revealing persistent phase transitions and their characteristics through analytical and numerical methods.

Contribution

It demonstrates the persistence of phase transitions in disordered spin chains with symmetry-preserving disorder using analytical and numerical approaches, including mapping to fermion chains and MPS simulations.

Findings

Transition persists under disorder in both models.

Analytical solution for the cluster-Ising model reveals edge mode changes.

Numerical evidence of phase transition in the Heisenberg chain.

Abstract

We study the robustness of non-local string order in two paradigmatic disordered spin-chain models, a spin-1/2 cluster-Ising and a spin-1 XXZ Heisenberg chain. In the clean case, they both display a transition from antiferromagnetic to string order. Applying a disorder which preserves the Hamiltonian symmetries, we find that the transition persists in both models. In the disordered cluster-Ising model we can study the transition analytically -- by applying the strongest coupling renormalization group -- and numerically -- by exploiting integrability to study the antiferromagnetic and string order parameters. We map the model into a quadratic fermion chain, where the transition appears as a change in the number of zero-energy edge modes. We also explore its zero-temperature-singularity behavior and find a transition from a non-singular to a singular region, at a point that is different from the one separating non-local and local ordering.} The disordered Heisenberg chain can be treated only numerically: by means of MPS-based simulations, we are able to locate the existence of a transition between antiferromagnetic and string-ordered phase, through the study of order parameters. Finally we discuss possible connections of our findings with many body localization.