Many-body localization at nonzero temperature is a quantum-phase transition that is of very fundamental interest to both many-body quantum physics and statistical mechanics. Non-Hermitian systems possess rich and unique phenomena that never are found in their Hermitian counterparts, such as unidirectional invisibility and enhanced sensitivity. In the present study, we explore many-body localization in periodically driven non-Hermitian lattices. The lattices are one-dimensional, and the drive is designed in a piecewise two-step form that consists of a uniform coherent tunneling and incommensurate onsite gain and loss. We find that the system can be in localized, delocalized, or mixed phases depending on the driving frequency and the phase shift of the complex potential. Two critical driving frequencies are identified; one corresponds to the largest phase shift of the complex potential that keeps all the quasienergy spectra real and the eigenstates extended, and the other one is established by the vanishing of all real spectra. We also find that a very weak complex potential can lead the system to localization, when the driving frequency is lower than the critical frequency. We show that in the high-frequency limit, the critical phase shift that separates the two regions with respectively a real and complex spectrum tends to a constant, and the constant can be determined by an effective non-Hermitian Hamiltonian.
Many-body localization at nonzero temperature is a quantum-phase transition that is of very fundamental interest to both many-body quantum physics and statistical mechanics. Non-Hermitian systems possess rich and unique phenomena that never are found in their Hermitian counterparts, such as unidirectional invisibility and enhanced sensitivity. In the present study, we explore many-body localization in periodically driven non-Hermitian lattices. The lattices are one-dimensional, and the drive is designed in a piecewise two-step form that consists of a uniform coherent tunneling and incommensurate onsite gain and loss. We find that the system can be in localized, delocalized, or mixed phases depending on the driving frequency and the phase shift of the complex potential. Two critical driving frequencies are identified; one corresponds to the largest phase shift of the complex potential that keeps all the quasienergy spectra real and the eigenstates extended, and the other one is established by the vanishing of all real spectra. We also find that a very weak complex potential can lead the system to localization, when the driving frequency is lower than the critical frequency. We show that in the high-frequency limit, the critical phase shift that separates the two regions with respectively a real and complex spectrum tends to a constant, and the constant can be determined by an effective non-Hermitian Hamiltonian.
The explorations of non-Hermiticity have been devoted to investigate the disorder-induced many-body localization (MBL). However, the sensitivity of the spatial boundary conditions and the interplay of the non-Hermitian skin effect with many-body phenomena are not yet clear. For a MBL system in the presence of nonreciprocal tunnelings and random disorder potential, we identify two different complex-real spectral transitions, one is present for both open and periodic boundaries while the other is present only for open boundaries of coupled non-Hermitian chains. The later is driven due to the interchain coupling at weak disorder where the level statistics of the real eigenenergy phase follows a Gaussian orthogonal ensemble. We further characterize wave functions through the (biorthogonal) inverse participation ratio and fractal dimension, which reveal the suppression of skin effect in the non-Hermitian MBL phase. Finally, we demonstrate that the quench dynamics of the local particle density, spin imbalance, and entanglement entropy also signify the hallmark of the boundary effects and nonergodic character of many-body localization.
The non-Hermitian skin effect (NHSE), featured by the collapse of bulk-band eigenstates into the localized boundary modes of the systems, is one of most striking properties in the fields of non-Hermitian physics. Unique physical phenomena related to the NHSE have attracted a lot of interest, however, their experimental realizations usually require nonreciprocal hopping, which faces a great challenge in ultracold-atom systems. In this work, we propose to realize the NHSE in a 1D optical lattice by periodically-driven ultracold atoms in the presence of staggered atomic loss. By studying the effective Floquet Hamiltonian in the high-frequency approximation, we reveal the underlying mechanism for the periodic-driving-induced the NHSE. We found that the robust NHSE can be tuned by driving phase, which is manifested by the dynamical localization. Most remarkably, we uncover the periodic-driving-induced critical skin effect for two coupled chains with different driving phases, accompanied by the appearance of size-dependent topological in-gap modes. Our studies provide a feasible way for observing the NHSE and exploring corresponding unique physical phenomena due to the interplay of non-Hermiticity and many-body statistics in ultracold-atom systems.
The non-Hermitian skin effect (NHSE), characterized by the collapse of bulk-band eigenstates into the localized boundary modes of the systems, is one of most striking properties in the field of non-Hermitian physics. Unique physical phenomena related to the NHSE have attracted a great deal of interest; however, their experimental realization usually requires nonreciprocal hopping, which faces a great challenge in ultracold-atom systems. In this work we propose the realization of the NHSE in a one-dimensional optical lattice by periodically driven ultracold atoms in the presence of staggered atomic loss. By studying the effective Floquet Hamiltonian in the high-frequency approximation, we reveal the underlying mechanism for the periodic-driving-induced NHSE. We find that the robust NHSE can be tuned by the driving phase, which is manifested by the dynamical localization. Most remarkably, we uncover the periodic-driving-induced critical skin effect for two coupled chains with different driving phases, accompanied by the appearance of size-dependent topological in-gap modes. Our study provides a feasible way to observe the NHSE and explore the corresponding unique physical phenomena due to the interplay of non-Hermiticity and many-body statistics in ultracold-atom systems.
We study the combined effect of quasiperiodic disorder, driven, and interaction in the periodically kicked Aubry-Andr\'e model. In the noninteracting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a dynamical localization transition in the high-frequency region, whereas the spectrum statistics becomes intricate in the low-frequency region due to the emergence of the extended/localized-to-multifractal edges in the quasienergy spectrum, which separate the multifractal states from the extended (localized) states. When the interaction is introduced, we find the periodically kicked incommensurate potential can lead to a transition from the ergodic to many-body-localization phase in the high-frequency region. However, the many-body localization phase vanishes in the low-frequency region even for the strong quasiperiodic disorder. Our studies demonstrate that the periodically kicked Aubry-Andr\'e model displays rich dynamical phenomena and the driving frequency plays an important role in the formation of many-body localization in addition to the disorder strength.
As a hallmark of a pure quantum effect, quantum entanglement has provided unconventional routes to characterize condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian quasicrystals. We study a class of experimentally realizable models for non-Hermitian quasicrystal chains, in which asymmetric hopping and complex potential coexist. We diagnose the global phase diagram by means of entanglement from both the real-space and momentum-space partitions. By measuring the entanglement entropy, we numerically determine the metal-insulator transition point. We combine real-space and momentum-space entanglement spectra to complementarily characterize the delocalization phase and the localization phase. Inspired by the entanglement spectrum, we further analytically prove that a duality exists between the two phase regions. The transition point is self-dual and exact, further validating the numerical result from diagonalizing non-Hermitian matrices. Finally, we identify the mobility edge by means of entanglement.
In the present study, the interplay among interaction, topology, quasiperiodicity, and non-Hermiticity is studied. The hard-core bosons model on a one-dimensional lattice with asymmetry hoppings and quasiperiodic onsite potentials is selected. This model, which preserves time-reversal symmetry (TRS), will exhibit three types of phase transition: Real-complex transition of eigenenergies, topological phase transition, and many-body localization (MBL) phase transition. For the real-complex transition, it is found that the imaginary parts of the eigenenergies are always suppressed by the MBL. Moreover, by calculating the winding number, a topological phase transition can be revealed with the increase of potential amplitude, and we find that the behavior is quite different from the single-particle systems. Based on our numerical results, we conjecture that these three types of phase transition occur at the same point in the thermodynamic limit, and the MBL transition of quasiperiodic system and disordered system should belong to different universality classes. Finally, we demonstrate that these phase transitions can profoundly affect the dynamics of the non-Hermitian many-body system.