Many-body phase transitions in a non-Hermitian Ising chain

• URL: http://arxiv.org/abs/2311.11251v2
• Date: Thu, 8 Aug 2024 11:13:23 GMT
• Title: Many-body phase transitions in a non-Hermitian Ising chain
• Authors: Chao-Ze Lu, Xiaolong Deng, Su-Peng Kou, Gaoyong Sun,
• Abstract summary: We study many-body phase transitions in a one-dimensional ferromagnetic transversed field Ising model with an imaginary field. We show that the system exhibits three phase transitions: one second-order phase transition and two $mathcalPT$ phase transitions.
• Score: 0.8749675983608172
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study many-body phase transitions in a one-dimensional ferromagnetic transversed field Ising model with an imaginary field and show that the system exhibits three phase transitions: one second-order phase transition and two $\mathcal{PT}$ phase transitions. The second-order phase transition occurring in the ground state is investigated via biorthogonal and self-normal entanglement entropy, for which we develop an approach to perform finite-size scaling theory to extract the central charge for small systems. Compared with the second-order phase transition, the first $\mathcal{PT}$ transition is characterized by the appearance of an exceptional point in the full energy spectrum, while the second $\mathcal{PT}$ transition only occurs in specific excited states. Furthermore, we interestingly show that both of exceptional points are second-order in terms of scalings of imaginary parts of the energy. This work provides an exact solution for many-body phase transitions in non-Hermitian systems.

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