Critical spin models from holographic disorder

TL;DR

This paper investigates how holographic disorder affects XXZ spin chains, revealing that certain critical phases maintain conformal properties despite quasiperiodic disorder, suggesting a new class of holography-inspired critical states.

Contribution

It demonstrates that holographic disorder preserves critical conformal behavior in XXZ spin chains, extending previous non-interacting models to more general Hamiltonians.

Findings

Disorder breaks translation invariance but preserves site-averaged correlations.

Entanglement entropy follows CFT scaling in disordered phases.

Critical behavior depends on the boundary disorder's relation to bulk hyperbolic tilings.

Abstract

Discrete models of holographic dualities, typically modeled by tensor networks on hyperbolic tilings, produce quantum states with a characteristic quasiperiodic disorder not present in continuum holography. In this work, we study the behavior of XXZ spin chains with such symmetries, showing that lessons learned from previous non-interacting (matchgate) tensor networks generalize to more generic Hamiltonians under holographic disorder: While the disorder breaks translation invariance, site-averaged correlations and entanglement of the disorder-free critical phase are preserved at a plateau of nonzero disorder even at large system sizes. In particular, we show numerically that the entanglement entropy curves in this disordered phase follow the expected scaling of a conformal field theory (CFT) in the continuum limit. This property is shown to be non-generic for other types of quasiperiodic disorder, only appearing when our boundary disorder ansatz is described by a "dual" bulk hyperbolic tiling. Our results therefore suggest the existence of a whole class of critical phases whose symmetries are derived from models of discrete holography.