Excited-state quantum phase transitions in systems with many interacting spins-1/2

Abstract

Excited-state quantum phase transitions (ESQPTs) are quantum phase transitions that take place at excited levels. They have been shown for different systems with few degrees of freedom. One of such models is the Lipkin-Meshkov-Glick (LMG) model, which has one degree of freedom and is equivalent to a spin-1/2 model with infinite-range interaction. Here, we examine whether the precursors of the ESQPT in the LMG model can still be captured when the long-range interaction in this spin system becomes finite and the Hilbert space exponentially large in system size.