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

Exact solutions for excited states in non-integrable quantum 
Hamiltonians have revealed novel dynamical phenomena that can occur in 
quantum many-body systems. In this talk, I will present a method to
analytically construct a specific set of volume-law-entangled exact 
excited eigenstates in a large class of spin Hamiltonians. In 
particular, I will show that all spin chains that satisfy a simple set 
of conditions host exact volume-law eigenstates in the middle of their 
spectra. This framework unifies many recent constructions of volume-law 
entangled eigenstates in the literature. Finally, I will show that a 
similar construction also generalizes to spin models on graphs in 
arbitrary dimensions.