We study an entanglement phase transition in a class of chaotic non-Hermitian spin chains whose spin-spin coupling terms commute with the non-Hermitian contributions. Two representative models are investigated: the transverse-field Ising model with a complex longitudinal field and the non-Hermitian XX model with a transverse field. By analyzing their complex spectra, we find that both models undergo a dissipation-induced gapless-gapped phase transition when the transverse field exceeds a model-dependent threshold. Interestingly, the complex gap does not vary monotonically with the dissipation rate; instead, it exhibits pronounced oscillations before entering the gapped phase. By simulating their non-unitary dynamics, we show that the steady-state entanglement entropy undergoes a transition from volume-law to area-law scaling as the dissipation rate increases. Moreover, several unexpected features emerge within the volume-law regime: a larger complex gap or dissipation rate may lead to a more entangled steady state. We trace these unusual behaviors of the complex gap and the steady-state entanglement to level crossings between the maximal imaginary level and other spectral levels. Our work uncovers an exotic entanglement transition in chaotic non-Hermitian many-body systems.
Abstract We study in this paper the quantum phase transition (QPT) from normal phase (NP) to superradiant phase (SP) for
N three-level atoms in a single-mode optical cavity for both Hermitian and non-Hermitian Hamiltonians, where the
Ξ-type three-level atom is described by spin-1 pseudo-spin operators. The long standing gauge-choice ambiguity of
A⋅p and
d⋅E called respectively the Coulomb and dipole gauges is reconciled by the time-dependent gauge transformation on the Schrödinger equation. Both
A⋅p and
d⋅E interactions are included in the unified gauge, which is truly gauge equivalent to the minimum coupling principle. The Coulomb and dipole interactions are just the special cases of unified gauge. Remarkably three interactions lead to the same results under the resonant condition of field-atom frequencies, while significant difference appears in red and blue detunings. The QPT is analyzed in terms of spin-coherentstate variational method, which indicates the abrupt changes of energy spectrum, average photon number as well as the atomic population at the critical point of interaction constant. Crucially, we reveal the sensitive dependence on the initial optical-phase, which is particularly useful to test the validity of three gauges experimentally. The non-Hermitian atom-field interaction results in the exceptional point (EP), beyond which the semiclassical energy function becomes complex. However the energy spectrum of variational ground state is real in the absence of EP, and does not become complex. The superradiant state is unstable due to the non-Hermitian interaction induced photon-number loss. Thus only the NP exists in the nonHermitian Dicke Model Hamiltonian.
We study the dynamical properties in a non-Hermitian Bose-Hubbard dimer and show that the steady state consists mostly of the eigenstate whose eigenvalue has the largest imaginary part. A sharp phase transition occurs in the steady state and the phase transition occurs for a finite particle number, not for infinite ones, in contrast to the Hermitian system. We also investigate the quantum Fisher information and entanglement in two different phases. The results show that the steady state in the Josephson oscillation regime is fully N -particle entangled and the corresponding parameter sensitivity approaches the Heisenberg limit. In the self-trapping regime, the parameter sensitivity just scales as the shot-noise limit. Moreover, quantum Fisher information of the steady state is robust to the initial state, which indicates that the non-Hermitian dynamics takes more advantage than the Hermitian one for quantum metrology.