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

• URL: http://arxiv.org/abs/2410.22773v1
• Date: Wed, 30 Oct 2024 07:41:21 GMT
• Title: Exact volume-law entangled eigenstates in a large class of spin models
• Authors: Sashikanta Mohapatra, Sanjay Moudgalya, Ajit C. Balram,
• Abstract summary: We analytically construct a specific set of volume-law-entangled exact excited eigenstates in a large class of spin Hamiltonians. We show that all spin chains that satisfy a simple set of conditions host exact volume-law eigenstates in the middle of their spectra. Our framework also unifies many recent constructions of volume-law entangled eigenstates in the literature.
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• 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 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 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.

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