Boundary effects in presence of dissipation in strongly correlated physics.

When a quantum system is not isolated but coupled to an environment its effective dynamics involves loss and gain typically described by a non-Hermitian Hamiltonian. Such loss plays an important role in many quantum systems. For example, in this Noisy Intermediate-Scale Quantum Computing era, it is crucial to understand how robust the many-body phenomena are in presence of dissipation. An important class of such systems is described by PT-symmetric non-Hermitian where loss and gain are balanced. Here we present an exact solution of a PT-symmetric non-Hermitian quantum spin chain and explore the effects due to the non-unitary dynamics. The model describes a realistic system of interacting spinless fermions chain where particles can hop into or out of the system at the edges. We identify different phases where PT symmetry is spontaneously broken and unbroken. We show that the boundary edge modes are robust to the loss to over a range of parameters and compute several observables.