An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics

TL;DR

This paper analyzes the folded XXZ spin chain, revealing its integrability, Hilbert space fragmentation, exact solutions, and unique dynamical properties, including persistent oscillations and connections to quantum field theory deformations.

Contribution

The paper provides a new derivation of the model's Hamiltonian, explores its integrability and fragmentation, and studies its exact solutions and dynamics, including novel interpretations and mappings.

Findings

Hilbert space fragmentation leads to exponential degeneracies.

Exact spectrum and thermodynamics are derived for the model.

Certain quenches result in persistent oscillations and breakdown of equilibration.

Abstract

We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties. The particles have constant scattering lengths, which leads to a simple treatment of the exact spectrum and the dynamics of the system. The Hilbert space of the model is fragmented, leading to exponentially large degeneracies in the spectrum, such that the exponent depends on the particle content of a given state. We provide an alternative derivation of the Hamiltonian and the conserved charges of the model, including a new interpretation of the so-called "dual model" considered earlier. We also construct a non-local map that connects the model with the Maassarani-Mathieu spin chain, also known as the SU(3) XX model. We consider the exact solution of the model with periodic and open boundary conditions, and also derive multiple descriptions of the exact thermodynamics of the model. We consider quantum quenches of different types. In one class of problems the dynamics can be treated relatively easily: we compute an example for the real time dependence of a local observable. In another class of quenches the degeneracies of the model lead to the breakdown of equilibration, and we argue that they can lead to persistent oscillations. We also discuss connections with the $T\bar T$- and hard rod deformations known from Quantum Field Theories.