PT-symmetry breaking in quantum spin chains with exceptional non-Hermiticities

Abstract

Since the realization of quantum systems described by non-Hermitian Hamiltonians with parity-time () symmetry, interest in non-Hermitian, quantum many-body models has steadily grown. Most studies to date map to traditional quantum spin models with a non-Hermiticity that arises from making the model parameters complex or purely imaginary. Here we present a set of models with non-Hermiticity generated by splitting a Hermitian term into two Jordan-normal form parts, and the perturbations are confined to one or two sites. We present exact diagonalization results for a finite threshold in such models and provide an analytical approach for understanding the numerical results. Surprisingly, with non-Hermitian potentials confined to two or even a single site, the threshold seems insensitive to the size of the quantum spin chain. Our results provide a pathway to experimentally feasible non-Hermitian quantum spin chains where the confluence of many-body effects and non-Hermiticity effects can be observed.