Quench Spectroscopy for Dissipative and (Non)-Hermitian Quantum Lattice Models

We extend the quench spectroscopy method to dissipative and isolated non-Hermitian quantum lattice models via the case study of the open Bose-Hubbard chain and the non-Hermitian transverse-field Ising chain respectively. We first investigate theoretically the dynamics of the open Bose-Hubbard chain confined in the superfluid phase induced by a sudden global quench on the dissipations and the repulsive interactions using the equation-of-motion approach. Using the same analytical approach, we then discuss the applicability of the quench spectroscopy to non-Hermitian quantum lattice models by considering the sudden global quench dynamics of the non-Hermitian transverse-field Ising chain confined in the paramagnetic phase. We finally generalize this spectroscopy method to isolated Hermitian quantum lattice models characterized by a quadratic fermionic or bosonic Hamiltonian. For this purpose, we consider the case study of the Hermitian version of the latter one-dimensional lattice model. The investigation is performed analytically for the bosonic and fermionic reformulations while considering for each case the equation-of-motion and quasiparticle theoretical approaches.