The correspondence between the real-complex transition in energy and delocalization-localization transition is well established in a class of Aubry-André-Harper model with exponential non-Hermitian on-site potentials. In this paper, we study a generalized Aubry-André model with off-diagonal modulation and non-Hermitian on-site potential. We find that, when there exists an incommensurate off-diagonal modulation, the correspondence breaks down, although the extended phase is maintained in a wide parameter range of the strengths of the on-site potential and the off-diagonal hoppings. An additional intermediate phase with a non-Hermitian mobility edge emerges when the off-diagonal hoppings become commensurate. This phase is characterized by the real and complex sections of the energy spectrum corresponding to the extended and localized states. In this case, the aforementioned correspondence reappears due to the recovery of the $\mathcal{PT}$ symmetry.

In this paper, the interplay between non-Hermiticity, quasidisorder, and repulsive interaction is studied for hard-core bosons confined in a one-dimensional optical lattice, where non-Hermiticity is induced by the nonreciprocal hoppings and the on-site gain and loss breaking the time-reversal symmetry. Although the energy spectra of the static system are fully complex, with the evolution of the initial state, the real part of the expectation value of the Hamiltonian under the time-evolved wave function changes stably. By means of the entanglement entropy and its dynamical evolution, as well as the inverse participation ratio, the many-body localization (MBL) is found to play the key role in the stability of the dynamical behavior of the real part of the expectation value, independent of whether the spectrum of the static Hamiltonian is real or complex. In the delocalization phase, the dynamical evolution of the real part of the expectation value is unstable. Meanwhile, the nearest-neighbor level spacings statistics shows the MBL transition accompanied by the transition from the Ginibre distribution to the complex Poisson distribution, different from the one in the time-reversal invariant system. In addition, the dynamical stability of the real part of the energy and the MBL transition can be characterized by the winding number, indicating that the MBL transition and the topological transition occur simultaneously, and the realization of the Hamiltonian is discussed.

Recently, there is an interest in studying the bulk-edge correspondence for nonlinear eigenvalue problems in a two-dimensional topological system with spin-orbit coupling. By employing the method of the auxiliary eigenvalues as introduced in T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024), the nonlinear bulk-edge correspondence was established. In this paper, taking the Haldane model as an example, we address that such a correspondence will appear in two-dimensional topological systems without spin-orbit coupling. The resulting edge states are characterized by the Chern number of the auxiliary energy band. A full phase diagram containing topological nontrivial phase, topological trivial phase, and metallic phase is obtained. Our work generalizes the study of the bulk-edge correspondence for nonlinear eigenvalue problems in two-dimensional systems.

A modified real-space-Pfaffian method is applied to characterize the topological superconducting transition of a one-dimensional p-wave superconductor with quasiperiodic potentials. We found that the Majorana zero-energy mode exists in the topological non-trivial phase, and its spatial distribution is localized at ends of the system, whereas in the topological trivial phase, there is no Majorana zero mode. Furthermore, we numerically found that due to the competition between the localized quasi-disorder and the extended p-wave pairing, there are mobility edges in the energy spectra. Our theoretical work enriches the research on the quasiperiodic p-wave superconducting models.

In this paper, a quasiperiodic system with off-diagonal and diagonal modulations is studied. By analyzing the inverse participation ratio and the centroid position of the wave packet, the delocalization-localization phase diagrams in the equilibrium state and the non-equilibrium steady state are obtained respectively. The stability of the system's initial state on dissipation and the dissipation-driven delocalization-localization transition (or vice versa) are discussed. The dynamic evolution behavior provides evidence for the existence of the quantum Mpemba effect in this dissipation-modulated system. A starting-line hypothesis is proposed, which can be used to explain the occurrence and absence of the quantum Mpemba effect. In addition, the thermodynamic applications of this system have also been studied. The results prove that the localized phase is beneficial to the realization of quantum heater as well. Our work has promoted the understanding of the steady-state phase transitions and dynamic behaviors of dissipation-modulated quasiperiodic systems, and has expanded the existing thermodynamic research on the application of quasiperiodic systems.

The Dicke-Hubbard model, describing an ensemble of interacting atoms in a cavity, provides a rich platform for exploring collective quantum phenomena. However, its potential for quantum thermodynamic applications remains largely uncharted. Here, we study a quantum Otto heat engine whose working substance is a system governed by the Dicke-Hubbard Hamiltonian. Through the research on steady-state superradiance phase transitions, it is demonstrated that the steady-state synergistic mechanism under high and low temperature environments is the reason for the emergence of high-performance heat engines. By analyzing the influences of atom-light coupling strength, inter-cavity hopping strength and atom number on the working modes of quantum Otto cycle, it is clarified that the effective working regions of each working mode. This work has established a close connection between superradiance phase transition and the quantum thermodynamic applications. It not only deepens our understanding of the energy conversion mechanism in non-equilibrium quantum thermodynamics but also lays a theoretical foundation for the future experimental design of high-performance quantum Otto heat engines.