Real-complex quantum phase transition in non-Hermitian disorder-free systems

Localization phenomena and the quantum phase transition are two core concepts of low-dimensional condensed-matter physics. The localization transition problem related to vortex line pinning in superconductors can be studied by mapping it to a real-complex non-Hermitian problem. Its relation to the quantum phase transition has to be discerned. We explore these two phase transitions induced by interactions rather than by the disorder in non-Hermitian systems. It is shown that the phase diagram is divided into the classical and quantum regimes by a characteristic temperature. The classical regime contains topological localization transitions and a tricritical point which connects the first-order phase transition line to the second-order transition line. The quantum regime is a nonchaotic and first-order phase transition. In such a quantum regime, the relaxation time does not always satisfy the bound on chaos. We show that the oscillation phase transition line due to quantized Matsubara frequencies can give an index similar in structure to the quantum oscillation in an imaginary magnetic field, which makes the first-order quantum phase diagram behave as a quantum critical phase diagram.