Hilbert Space Fragmentation and Ashkin-Teller Criticality in Fluctuation Coupled Ising Models

TL;DR

This paper explores how Hilbert space fragmentation influences phase transitions in coupled Ising models, revealing a connection to Ashkin-Teller universality and explaining pseudo-first order behavior in related classical models.

Contribution

It introduces the concept of Hilbert space fragmentation affecting phase transitions in coupled Ising models and links this to Ashkin-Teller criticality, supported by quantum Monte Carlo simulations.

Findings

Bounded dynamics within spatial partitions due to quantum fluctuations

Weak mixing leads to local order without long-range order

Explanation for pseudo-first order behavior in classical frustrated models

Abstract

We discuss the effects of exponential fragmentation of the Hilbert space on phase transitions in the context of coupled ferromagnetic Ising models in arbitrary dimension with special emphasis on the one dimensional case. We show that the dynamics generated by quantum fluctuations is bounded within spatial partitions of the system and weak mixing of these partitions caused by global transverse fields leads to a zero temperature phase with ordering in the local product of both Ising copies but no long range order in either species. This leads to a natural connection with the Ashkin-Teller universality class for general lattices. We confirm this for the periodic chain using quantum Monte Carlo simulations. We also point out that our treatment provides an explanation for pseudo-first order behavior seen in the Binder cumulants of the classical frustrated $J_1-J_2$ Ising model and the $q=4$ Potts model in 2D.