Phase Diagrams of Non-Hermitian Quantum Ising Chains

Quantum spin chains with parity-time (PT) symmetric Hamiltonians can provide a pathway to experimentally realizable non-Hermitian quantum materials. We investigate the phase diagram of Ising and Heisenberg spin chains with periodic boundary conditions and non-Hermitian potentials \sigma_\pm on only one or two sites. In contrast to anti-Hermitian potentials such as i\gamma\sigma_z, these exceptional potentials do not create an energy scale. We present exact diagonalization results for PT-symmetry breaking threshold, where the eigenvalues of the non-Hermitian Hamiltonian change from real to complex-conjugate pairs, and discuss the changes in correlation functions across this transition.