Non-Hermitian Ising model at finite temperature

Abstract

As a very simple model, the Ising model plays an important role in statistical physics. In the paper, with the help of quantum Liouvillian statistical theory, we study the one-dimensional non-Hermitian Ising model at finite temperature and give its analytical solutions. We find that the non-Hermitian Ising model shows quite different properties from those of its Hermitian counterpart. For example, the ‘pseudo-phase transition’ is explored between the ‘topological’ phase and the ‘non-topological’ phase, at which the Liouvillian energy gap is closed rather than the usual energy gap. In particular, we point out that the one-dimensional non-Hermitian Ising model at finite temperature can be equivalent to an effective anisotropic XY model in the transverse field. This work will help people understand quantum statistical properties of non-Hermitian systems at finite temperatures.