Exact volume-law entangled zero-energy eigenstates in a large class of spin models

TL;DR

This paper introduces a method to analytically construct volume-law-entangled zero-energy eigenstates in a broad class of spin models, revealing their thermal nature and unifying previous approaches.

Contribution

It provides a general analytical framework for constructing exact volume-law zero-energy eigenstates in various spin Hamiltonians, including models on arbitrary graphs.

Findings

All spin chains satisfying certain conditions host exact volume-law zero-energy eigenstates.

These eigenstates are highly atypical but thermal with respect to local observables.

The construction generalizes to spin models on graphs in any dimension.

Abstract

Exact solutions for excited states in non-integrable quantum Hamiltonians have revealed novel dynamical phenomena that can occur in quantum many-body systems. This work proposes a method to analytically construct a specific set of volume-law-entangled zero-energy exact excited eigenstates in a large class of spin Hamiltonians. In particular, we show that all spin chains that satisfy a simple set of conditions host exact volume-law zero-energy eigenstates in the middle of their spectra. Examples of physically relevant spin chains of this type include the transverse-field Ising model, PXP model, spin-$S$ $XY$ model, and spin-$S$ Kitaev chain. Although these eigenstates are highly atypical in their structure, they are thermal with respect to local observables. Our framework also unifies many recent constructions of volume-law entangled eigenstates in the literature. Finally, we show that a similar construction also generalizes to spin models on graphs in arbitrary dimensions.