Peak-valley mechanism for Hilbert space fragmentation

TL;DR

This paper introduces the peak-valley (PV) mechanism for Hilbert space fragmentation in one-dimensional integer spin chains, providing a unified framework to understand existing models and construct new strongly fragmented systems.

Contribution

The authors propose a simple local rule called PV fragmentation that explains and generalizes strong Hilbert space fragmentation in quantum spin chains.

Findings

PV fragmentation explains known strong HSF models.

It enables systematic construction of new fragmented models.

The framework applies to higher-spin systems and identifies higher-order HSF models.

Abstract

Ergodicity breaking in isolated systems has emerged as an important frontier in the study of quantum many-body physics. While generic Hamiltonians are expected to obey the eigenstate thermalization hypothesis (ETH), recent studies on Hilbert space fragmentation (HSF) have revealed possible robust nonthermal behavior even in disorder-free systems. Although numerous models exhibiting strong HSF are already known, existing analyses are typically model dependent, and a general organizing principle remains elusive. In this work, we introduce a simple mechanism for achieving strong HSF in one-dimensional integer spin chains, which we term "peak-valley (PV) fragmentation". The key idea is to devise a simple local rule which ensures the spin states in the computational basis can be labeled by a set of emergent good quantum numbers corresponding to the heights and depths of alternating peaks and valleys in a geometrical representation. We demonstrate that some known examples of strong HSF models, as well as their variants which break the HSF property, can be understood within the framework of PV fragmentation. Our approach also enables systematic construction of new fragmented models in higher-spin systems, and allows us to identify higher-order HSF models.