Phase transition in the PT-symmetric spin-1/2 quantum chain

We study a PT-symmetric spin-1/2 chain in which spins are located at the vertices connected and exchange interact along links. The model presented has exact solution for arbitrary values of the exchange integrals. The ground-state phase diagram consists of two states with different static Z2 gauge fields; all Z2 charges are equal to +1 or −1. These states are separated by a quantum critical point ψc = π/4, ψc is a critical value of the phase, that defines the PT-symmetric exchange interactions of spins inside the cell. The single-particle spectrum of the Majorana fermions in the sectors with uniform fluxes is defined by flat-band fermion states at ψ = 0, π/2 and band states at 0 < ψ < π/2. We also give a detailed analysis of the zero-temperature phase diagram of the model and demonstrate how this unusual phase transition arises. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'. (paper)