2024/10/30 by Mohapatra, Sashikanta, Moudgalya, Sanjay, Balram, Ajit C. · 5 citations
#FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2410.22773
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.