Survival of Hermitian Criticality in the Non-Hermitian Framework

Abstract

In this work, we investigate many-body phase transitions in a one-dimensional anisotropic XY model subject to a complex-valued transverse field. Within the biorthogonal framework, we calculate the ground-state correlation functions and entanglement entropy, confirming that their scaling behavior remains identical to that in the Hermitian XY model. The preservation of Hermitian phase transition features in the non-Hermitian setting is rooted in the persistence and emergence of symmetries and their breaking. Specifically, the ferromagnetic (FM) phase arises from the breaking of a $Z_2$ symmetry, while the Luttinger liquid (LL) phase is enabled by the emergence of a $U(1)$ symmetry together with the degeneracy of the real part of the energy spectrum. The nontrivial topology of the LL phase are characterized by the winding number around the exceptional point (EP). Given that non-Hermitian systems are inherently open, this research opens a new avenue for exploring conventional quantum phase transitions that are typically vulnerable to decoherence and environmental disruption in open quantum systems.

9 pages, 5 figures, 1 table

References in corpus (16)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Non-Hermitian Topology and Exceptional-Point Geometries
• Non-Hermitian topological phenomena: A review
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Non-Hermitian chiral phononics through optomechanically-induced squeezing
• Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems
• Quantum Phase Transitions in Optomechanical Systems
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Quantum phase transition in a non-Hermitian XY spin chain with global complex transverse field
• Many-body phase transitions in a non-Hermitian Ising chain
• Biorthogonal topological charge pumping in non-Hermitian systems
• Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Biorthogonal Neural Network Approach to Two-Dimensional Non-Hermitian Systems