Hilbert space fragmentation in quantum Ising systems induced by side coupling

TL;DR

This paper investigates how Hilbert space fragmentation and quantum scars emerge in quantum Ising systems with side coupling, especially near resonance conditions, through analytical and numerical methods.

Contribution

It reveals the conditions under which Hilbert space fragmentation occurs in coupled quantum Ising systems and analyzes the emergence of quantum scars at resonance.

Findings

Hilbert space fragments into exponentially many sectors at resonance.

Quantum scars are more pronounced near resonance conditions.

Numerical simulations confirm the analytical predictions across various lattice geometries.

Abstract

We study Hilbert space fragmentation and quantum scars in quantum spin systems with Ising interactions. The system consists of two sets of quantum spins, A and B. As the parent system, set A is an Ising model on arbitrary lattices with a transverse field, while set B comprises free spins that are coupled to set A. We show that the Hilbert space is fragmented into exponentially many decoupled sectors when the transverse field and the side coupling strength are at resonance. As examples, several typical systems with quantum scars are studied analytically. Numerical simulations of probability distribution of entanglement entropy for finite-size chains, square and triangular lattices are performed using the Monte Carlo method. The results show that Hilbert space fragmentation and the corresponding quantum scars become pronounced when the system approaches resonance.