Dynamical signatures and steady state behaviour of periodically driven non-Hermitian Ising chain

Abstract

We have tried to describe how the interplay between the system environment coupling and external driving frequency shapes the dynamical properties and steady state behavior in a periodically driven transverse field Ising chain subject to measurement. We have analyzed the fate of the steady state entanglement scaling properties as a result of a measurement induced phase transition. We have explained how such steady state entanglement scaling can be computed analytically using asymptotic features of the determinant of associated correlation matrix which turned out to be of block Toeplitz form. We have pointed out the differences from the Hermitian systems in understanding the entanglement scaling behav-ior in regimes where the asymptotic analysis can be performed using Fisher-Hartwig con-jecture. Finally we have discussed how the tuning of the drive frequency controls the do- main of applicability of the Fisher-Hartwig conjecture and the emergence of the long range ordering of the effective Floquet Hamiltonian governing the properties of the system.