Exact volume-law entangled zero-energy eigenstates in a large class of spin models
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- model, and spin- 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.
Keywords
Cite
@article{arxiv.2410.22773,
title = {Exact volume-law entangled zero-energy eigenstates in a large class of spin models},
author = {Sashikanta Mohapatra and Sanjay Moudgalya and Ajit C. Balram},
journal= {arXiv preprint arXiv:2410.22773},
year = {2025}
}