We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a Hermitian Fermi gas. The fermionic Green's function decays in a power law fashion for large distances, as expected from gapless excitations, although the exponent is reduced from -1 due to the quantum Zeno effect. In spite of the gapless nature of the excitations, the ground state entanglement entropy saturates to a finite value, independent of the subsystem size due to the non-Hermitian correlation length intrinsic to the system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or opens up a gap and protects PT symmetry, respectively. Our results challenge the concept of universality in non-Hermitian systems, where quantum criticality can be masked due to non-Hermiticity.
We investigate the decay of spatial correlations of
PT-symmetric non-Hermitian one-dimensional models that host higher-order exceptional points. Beyond a certain correlation length, they develop anomalous power-law behavior that indicates strong suppression of correlations in the non-Hermitian setups as compared to the Hermitian ones. The correlation length is also reflected in the entanglement entropy where it marks a change from logarithmic growth at short distance to a constant value at large distance, characteristic of an insulator, despite the spectrum being gapless. Two different families of models are investigated, both having a similar spectrum constrained by particle-hole symmetry. The first model offers an experimentally attractive way to generate arbitrary higher-order exceptional points and represents a non-Hermitian extension of the Dirac Hamiltonian for general spin. At the critical point, it displays a decay of the correlations $\ensuremath{\sim}1/{x}^{2}$ and
1/x3 irrespective of the order of the exceptional point. The second model is constructed using unidirectional hopping and displays enhanced suppression of correlations $\ensuremath{\sim}1/{x}^{a}, a\ensuremath{\ge}2$ with a power law that depends on the order of the exceptional point.
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.
We investigate a quantum quench from a critical to an exceptional point. The initial state, prepared in the ground state of a critical Hermitian system, is time evolved with a non-Hermitian SSH model, tuned to its exceptional point. The single particle density matrix exhibits supersonic modes and multiple light cones, characteristic of non-Hermitian time evolution. These propagate with integer multiples of the original Fermi velocity. In the long time limit, the fermionic Green's function decays spatially as
1/x2, in sharp contrast to the usual
1/x decay of noninteracting fermions. The entanglement entropy is understood as if all these supersonic modes arise from independent quasiparticles (though they do not), traveling with the corresponding supersonic light cone velocity. The entropy production rate decreases with time and develops plateaus during the time evolution, signaling the distinct velocities in the propagation of nonlocal quantum correlations. At late times, the entanglement entropy saturates to a finite value, satisfying a volume law.
Conformal invariance often accompanies criticality in Hermitian systems. However, its fate in non-Hermitian settings is less clear, especially near exceptional points where the Hamiltonian becomes non-diagonalizable. Here we investigate whether a 1+1-dimensional gapless non-Hermitian system can admit a conformal description, focusing on a PT-symmetric free-fermion field theory. Working in the biorthogonal formalism, we identify the conformal structure of this theory by constructing a traceless energy-momentum tensor whose Fourier modes generate a Virasoro algebra with central charge
c=−2. This yields a non-Hermitian, biorthogonal realization of a logarithmic conformal field theory, in which correlation functions exhibit logarithmic scaling and the spectrum forms Virasoro staggered modules that are characterized by universal indecomposability parameters. We further present a microscopic construction and show how the same conformal data (with finite-size corrections) can be extracted from the lattice model at exceptional-point criticality, thereby supporting the field-theory prediction.
The PT -symmetric non-Hermitian systems have been widely studied and explored both in theory and in experiment due to their various interesting features.In this work we focus on the dynamical features of a triplequbit system, one of which evolves under a local PT -symmetric Hamiltonian.An abnormal dynamic pattern in the entropy evolution process is identified that presents a parameter-dependent stable state, determined by the non-Hermiticity of Hamiltonian in the broken phase of PT symmetry.The entanglement and mutual information of a two-body subsystem can increase beyond the initial values, which do not exist in the Hermitian and two-qubit PT -symmetric systems.Moreover, an experimental demonstration of the stable states in non-Hermitian systems with nonzero entropy and entanglement is realized on a four-qubit quantum simulator with nuclear spins.Our work reveals the distinctive dynamic features in the triple-qubit PT -symmetric system and paves the way for practical quantum simulation of multiparty non-Hermitian system on quantum computers.