In this manuscript, we study the non-Hermitian spin-1/2 XY model in the presence of the alternating, imaginary and transverse magnetic fields. For the two-site spin system, we solve exactly the energy spectrum and phase diagram, also calculate the ground-state and thermal entanglements by using the concept of the concurrence. It is found that the two-site concurrence in the eigenstate which only depends on the imaginary magnetic field η is always equal to one in the region of PT symmetry, while it decreases with η in the PT-symmetric broken region. Especially, the concurrence shows the non-analytic behavior at the exceptional point, and the same is true in the case of the biorthogonal basis, which indicates that the concurrence can characterize the phase transition in this non-Hermitian system. The interesting thing is that η weakens the thermal entanglement when the system is isotropic and enhances the entanglement when the system becomes the Ising model. For the one-dimensional spin chain, the magnetization and entanglement are further studied by using the two-spin cluster mean-field approximation. The results show that their variations have opposite trends with the magnetic fields. Moreover, the system exists the first-order quantum phase transitions for some anisotropic parameters in the PT-symmetry region, and the entanglement changes suddenly at the quantum phase transition point.
Abstract In this manuscript, we explore the properties of a non-Hermitian spin-1/2 XY model subjected to alternating imaginary and transverse magnetic fields. Focusing on a two-spin system, we systematically construct the ground state phase diagram and provide an exact calculation of the ground state entanglement via the Negativity measure. Our findings reveal that, within eigenstates influenced by the anisotropy parameter, real magnetic fields, and imaginary magnetic fields, the anisotropy parameter significantly enhances entanglement, whereas the real magnetic field tends to diminish or even annihilate it. Notably, in the ΡΤ-symmetry broken phase, quantum entanglement demonstrates increased resilience to variations in the real magnetic field with the strengthening of the imaginary magnetic field. For eigenstates governed purely by the imaginary magnetic field, we observe that the two-spin entanglement remains maximal (i.e., value of 1) within the ΡΤ-symmetry region, while it gradually declines in the ΡΤ-symmetry broken region as the parameter η0 decreases. An intriguing observation is that the first derivative of the Negativity shows non-analytic behavior at the critical points, highlighting the role of Negativity as a reliable and effective indicator of phase transitions in this non-Hermitian system.
We study the quantum entanglement and quantum phase transition of the non-Hermitian anisotropic spin-
21 XY model and XXZ model with the staggered imaginary field by analytical methods and numerical exact diagonalization, respectively. Various entanglement measures, including concurrence, negativity, mutual information, and quantum coherence, and both biorthogonal and self-normal quantities are investigated. Both the biorthogonal and self-normal entanglement quantities, except the biorthogonal concurrence, are found to be capable of detecting the first-order and
PT transitions in the XXZ model, as well as the Ising and
RT transitions in the XY model. In addition, we introduce the unconstrained concurrence and demonstrate its effectiveness in detecting these transitions. On the other hand, the Berezinskii-Kosterlitz-Thouless (BKT) transition in the XXZ model is revealed through concurrence and negativity at small non-Hermiticity strengths. Notably, the critical points observed in the Hermitian limit evolve into exceptional points as the strength of the non-Hermiticity increases. Furthermore, we find that the first-order transition survives up to a higher non-Hermiticity strength compared to the BKT transition within the
PT-symmetric regime of the XXZ model.
Non-Hermitian spin systems have attracted extensive interest due to their unconventional magnetic properties, rich entanglement resources, and unusual quantum criticality phenomena. In this paper, based on the exact solution of a one-dimensional non-Hermitian spin-1/2 XY model with rotation-time-reversal (
RT) symmetry [X. Z. Zhang et al., Phys. Rev. A 87, 012114 (2013)], we study the ground-state energy density, magnetization, correlation functions, quantum entanglement, and correlation in
RT-symmetric and
RT-broken phases as well as their characteristics at the exceptional point. We find that the energy density rises faster with the non-Hermitian parameter $|\ensuremath{\gamma}|$ in the symmetric region than in the broken one and is elevated rapidly at the exceptional point, and the decay of magnetization has similar results. We analyze the effect of $\ensuremath{\gamma}$ on the system and find that the energy density decreases linearly with the external magnetic field
h for $\ensuremath{\gamma}>0,$ while it is bifurcated when $\ensuremath{\gamma}=0$. In addition, the behaviors of the energy density indicate that the phase transition caused by symmetry breaking is second order, which is further demonstrated by the magnetization, quantum entanglement, etc. The numerical results of the correlation functions surprisingly indicate that the
RT-broken phase has quasi-long-range order, which is quite different from the Hermitian XY model. Especially, the crossover behavior of the ground-state entanglement shows that it increases with $\ensuremath{\gamma}$ in the symmetric region, which is opposite to the case of the broken one, and its maximum always appears at the exceptional point. The above behaviors at the phase boundary are actually ascribed to the fierce competition between $\ensuremath{\gamma}$ and
h, which results in a rapid decline of magnetization and the appearance of the maximum of entanglement.
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
Z2 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.
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 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 transition is characterized by the appearance of an exceptional point in the full energy spectrum, while the second
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.
The characterization of the quantum critical properties of genuine non-Hermitian many-body systems remains ambiguous as neither the state considered nor the definition of expectation values is unique. In this work, we investigate the quantum critical properties of two models of non-Hermitian XY spin chains with magnetic field. Using exact solutions, we systematically investigate the parameter dependence of the energy, the magnetization as well as the long-distance asymptotic behavior of static correlation functions. We compute expectation values within the standard formalism of quantum mechanics as well as within biorthogonal quantum mechanics and take two different states which one might reasonably consider to be the analog of the ground state of a Hermitian model. The critical properties, including such fundamental characteristics as the phase diagram, depend on both the formalism used as well as the state considered. We provide arguments in favor of the use of standard quantum mechanics. Which state to be taken in computations, depends on the (hypothetical) experimental preparation of the system.