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.

arXiv comment9 pages, 5 figures, 1 table

References in corpus (38)

• Topological Insulators
• Topological insulators and superconductors
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Scaling of Entanglement close to a Quantum Phase Transitions
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Entanglement spectrum of a topological phase in one dimension
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Quantum phase transitions
• Non-Hermitian Topology and Exceptional-Point Geometries
• Biorthogonal Quantum Mechanics
• Universality of Entropy Scaling in 1D Gap-less Models
• Non-Hermitian topological phenomena: A review
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Knots and Non-Hermitian Bloch Bands
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays
• Non-Hermitian chiral phononics through optomechanically-induced squeezing
• Many-body approach to non-Hermitian physics in fermionic systems
• Observation of a non-Hermitian phase transition in an optical quantum gas
• Entanglement in non-unitary quantum critical spin chains
• Phase Transitions and Generalized Biorthogonal Polarization in Non-Hermitian Systems
• 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