Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field

TL;DR

This paper reveals that in higher-dimensional Ising models with a weak transverse field, the system exhibits Hilbert space fragmentation and ergodicity breaking, leading to complex non-equilibrium dynamics dependent on initial states.

Contribution

It demonstrates for the first time the emergence of Hilbert space fragmentation and ergodicity breaking in higher-dimensional Ising models with a weak transverse field.

Findings

Hilbert space fragmentation occurs in $d extgreater 1$ Ising models.

Ergodicity breaks down in a prethermal regime.

Nontrivial initial-state dependence in dynamics.

Abstract

The transverse-field Ising model is one of the fundamental models in quantum many-body systems, yet a full understanding of its dynamics remains elusive in higher than one dimension. Here, we show for the first time the breakdown of ergodicity in $d$-dimensional Ising models with a weak transverse field in a prethermal regime. We demonstrate that novel Hilbert-space fragmentation occurs in the effective non-integrable model with $d\geq2$ as a consequence of only one emergent global conservation law of the domain wall number. Our results indicate nontrivial initial-state dependence for non-equilibrium dynamics of the Ising models in a weak transverse field.