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arXiv:2311.11251 · Physical review. B./Physical review. B

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

Chao-Ze Lu, Xiaolong Deng, Su-Peng Kou, Gaoyong Sun

Published Jul 29, 2024• 16 citations
arXivHTMLPDF

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 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.

DOI
10.1103/physrevb.110.014441

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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 PT\mathcal{PT}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 PT\mathcal{PT}PT transition is characterized by the appearance of an exceptional point in the full energy spectrum, while the second PT\mathcal{PT}PT transition only occurs in specific excited states. Furthermore, we interestingly show that both 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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