Geometric phase of quenched spin models

Abstract

We consider a one dimensional spin-1/2 many body systems which initial state is a symmetry broken ground state and in which an evolution is induced by a sudden quench of the Hamiltonian parameters. We show that the long-time behavior of the spin state, can be approximated by the one of an open two level system in which the evolution preserves all the symmetries of the Hamiltonian. Exploiting such a result we analyze the geometric phase associated with the evolution of the single spin state and we prove analytically that its long-time behavior depends on the physical phase realized after the quench. When the system arrives in a paramagnetic phase, the geometric phase shows a periodicity that is absent in the other cases. Such a difference also survives in finite size systems until boundary effects come into play. We also discuss the effects of a explicit violation of the parity symmetry of the Hamiltonian and possible applications to the problem of the entanglement thermalization.

n-cluster models in a transverse magnetic field

“…(2018) 063103 reduces to the standard magnetic one. The presence of these two important novel phases candidate the n-cluster model in the external field as an interesting toy model to study hot topics of the current research, such as the presence of global entanglement [55] or the eects of a sudden quench of the Hamiltonian parameters [19,56].…”