The mobility edge (ME) is a fundamental concept in the Anderson localized systems, which marks the energy separating extended and localized states. Although the ME and localization phenomena have been extensively studied in non-Hermitian (NH) quasiperiodic tight-binding models, they remain limited to NH continuum systems. Here, we investigate the ME and localization properties of a one-dimensional (1D) NH quasiperiodic continuous system, which is described by a Schr{ö}dinger equation with an imaginary vector potential and an incommensurable one-site potential. We find that the ME is located in the real spectrum and falls between the localized and extended states. Additionally, we show that under the periodic boundary condition, the energy spectrum always exhibits an open curve representing high-energy extended electronic states characterized by a non-zero integer winding number. This complex spectrum topology is closely connected with the non-Hermitian skin effect (NHSE) observed under open boundary conditions, where the eigenstates of the bulk bands accumulate at the boundaries. Furthermore, we analyze the critical behavior of the localization transition and obtain critical potential amplitude accompanied by the universal critical exponent $ν\simeq 1/3$. Our study provides valuable inspiration for exploring MEs and localization behaviors in NH quasiperiodic continuous systems.
We investigate localization properties in a two-coupled uniform chains with quasiperiodic modulation on interchain coupling strength. We demonstrate that this ladder is equivalent to a Aubry-Andre (AA) chain when two legs are symmetric. Analytical and numerical results indicate the appearance of mobility edges for asymmetric ladder. We also propose an easily engineered quasiperiodic ladder system which is a moiré superlattice system consisting of two-coupled uniform chains. An irrational lattice constant difference results in quasiperiodic structure. Numerical simulations show that such a syst…
Quantum localization in 1D non-Hermitian systems, especially the search for exact single-particle mobility edges, has attracted considerable interest recently. While much progress has been made, the available methods to determine the ME of such models are still limited. In this work, we propose a new method to determine the exact mobility edge in a large class of 1D non-Hermitian quasiperiodic models with parity-time ($\mathcal{PT}$) symmetry. We illustrate our method by studying a specific model. We first use our method to determine the energy-dependent mobility edge as well as the spectrum f…
The mobility edges (MEs) in energy which separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic results which allow for an exact understanding are rare. Here we uncover a class of exactly solvable 1D models with MEs in the spectra, where quasiperiodic on-site potentials are inlaid in the lattice with equally spaced sites. The analytical solutions provide the exact results not only for the MEs, but also for the localization and extended features of …
We uncover the relationship of topology and disorder in a one-dimensional Su-Schrieffer-Heeger chain subjected to a slowly varying quasi-periodic modulation. By numerically calculating the disorder-averaged winding number and analytically studying the localization length of the zero modes, we obtain the topological phase diagram, which implies that the topological Anderson insulator (TAI) can be induced by a slowly varying quasi-periodic modulation. Moreover, unlike the localization properties in the TAI phase caused by random disorder, mobility edges can enter into the TAI region identified b…
We study a one-dimensional $p$-wave superconductor subject to non-Hermitian quasiperiodic potentials. Although the existence of the non-Hermiticity, the Majorana zero mode is still robust against the disorder perturbation. The analytic topological phase boundary is verified by calculating the energy gap closing point and the topological invariant. Furthermore, we investigate the localized properties of this model, revealing that the topological phase transition is accompanied with the Anderson localization phase transition, and a wide critical phase emerges with amplitude increments of the non…
We investigate localization-delocalization transition in one-dimensional non-Hermitian quasiperiodic lattices with exponential short-range hopping, which possess parity-time ($\mathcal{PT}$) symmetry. The localization transition induced by the non-Hermitian quasiperiodic potential is found to occur at the $\mathcal{PT}$-symmetry-breaking point. Our results also demonstrate the existence of energy dependent mobility edges, which separate the extended states from localized states and are only associated with the real part of eigen-energies. The level statistics and Loschmidt echo dynamics are al…
Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate bands of localized states from bands of critical states in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multi…
We introduce a self-consistent theory of mobility edges in nearest-neighbour tight-binding chains with quasiperiodic potentials. Demarcating boundaries between localised and extended states in the space of system parameters and energy, mobility edges are generic in quasiperiodic systems which lack the energy-independent self-duality of the commonly studied Aubry-André-Harper model. The potentials in such systems are strongly and infinite-range correlated, reflecting their deterministic nature and rendering the problem distinct from that of disordered systems. Importantly, the underlying theore…
We aim to study a one-dimensional $p$-wave superconductor with quasiperiodic on-site potentials. A modified real-space-Pfaffian method is applied to calculate the topological invariants. We confirm that the Majorana zero mode is protected by the nontrivial topology the topological phase transition is accompanied by the energy gap closing and reopening. In addition, we numerically find that there are mobility edges which originate from the competition between the extended $p$-wave pairing and the localized quasi-disorder. We qualitatively analyze the influence of superconducting pairing paramet…
We investigate the topology and localization of one-dimensional Hermitian and non-Hermitian Su-Schrieffer-Heeger chains with quasiperiodic hopping modulations. In the Hermitian case, phase diagrams are obtained by numerically and analytically calculating various topological and localization characters. We show the presence of topological extended, intermediate, and localized phases due to the coexistence of independent topological and localization phase transitions driven by the quasiperiodic disorder. Unlike the gapless and localized TAI phase in one-dimensional random disordered systems, we …
Uncorrelated disorder potential in one-dimensional lattice definitely induces Anderson localization, while quasiperiodic potential can lead to both localized and extended phases, depending on the potential strength. We investigate the Anderson localization in one-dimensional lattice with nonHermitian complex disorder and quasiperiodic potential. We present a non-Hermitian SSH chain to demonstrate that a nonzero imaginary disorder on-site potential can induce the standard Anderson localization. We also show that the non-Hermitian Aubry-Andre (AA) model exhibits a transition in parameter space, …
We demonstrate the existence of generalized Aubry-André self-duality in a class of non-Hermitian quasi-periodic lattices with complex potentials. From the self-duality relations, the analytical expression of mobility edges is derived. Compared to Hermitian systems, mobility edges in non-Hermitian ones not only separate localized from extended states, but also indicate the coexistence of complex and real eigenenergies, making it possible a topological characterization of mobility edges. An experimental scheme, based on optical pulse propagation in synthetic photonic mesh lattices, is suggested …
Engineering exact mobility edges in quasiperiodic Aharonov-Bohm chains
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
Department of Physics and Astronomy, National Institute of Technology, Rourkela（鲁尔基国家技术大学物理与天文系）；School of Physical Sciences, National Institute of Science Education and Research（科学教育与研究国立研究院物理科学学院）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
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 thereal-complex transition, it is found that the imaginary parts of the eigenenergies are always suppressed by the MBL. Moreov…
Anomalous mobility edges and extended-localized transition in a quasiperiodic emitter-cavity array
School of Physics and Optoelectronic Engineering & Institute of Theoretical Physics, Ludong University（鲁东大学物理与光电工程学院暨理论物理研究所）；Center for Quantum Sciences, Northeast Normal University（东北师范大学量子科学中心）
We study the stability of the topological phase in one-dimensional Su-Schrieffer-Heeger chain subject to the quasiperiodic hopping disorder. We investigate two different hopping disorder configurations, one is the Aubry-André quasiperiodic disorder without mobility edges and the other is the slowly varying quasiperiodic disorder with mobility edges. With the increment of the quasiperiodic disorder strength, the topological phase of the system transitions to a topologically trivial phase. Interestingly, we find the occurrence of the topological phase transition at the critical disorder strength…
Noise-Induced Resurrection of Dynamical Skin Effects in Quasiperiodic Non-Hermitian Systems
School of Physics, Peking University（北京大学物理学院）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
In this paper, we study a one-dimensional tight-binding model with tunable incommensurate potentials. Through the analysis of the inverse participation rate, we uncover that the wave functions corresponding to the energies of the system exhibit different properties. There exists a critical energy under which the wave functions corresponding to all energies are extended. On the contrary, the wave functions corresponding to all energies above the critical energy are localized. However, we are surprised to find that the critical energy is a constant independent of the potentials. We use the self-…
We analytically determine the non-Hermitian mobility edges of a one-dimensional quasiperiodic lattice model with exponential decaying hopping and complex potentials as well as its dual model, which is just a non-Hermitian generalization of the Ganeshan-Pixley-Das Sarma model with nonreciprocal nearest-neighboring hopping. The presence of non-Hermitian term destroys the self-duality symmetry and thus prevents us exploring the localization-delocalization point through looking for self-dual points. Nevertheless, by applying Avila's global theory, the Lyapunov exponent of the Ganeshan-Pixley-Das S…
Exact mobility rings in non-Hermitian quasiperiodically decorated Lieb lattices
College of Mathematics and Physics, Chengdu University of Technology（成都理工大学数学与物理学院）；School of Physics, Hangzhou Normal University（杭州师范大学物理学院）；School of Physics, Nankai University（南开大学物理学院）
Entanglement growth and information capacity in a quasiperiodic system with a single-particle mobility edge
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
We study a one-dimensional lattice model subject to non-Hermitian quasiperiodic potentials. Firstly, we strictly demonstrate that there exists an interesting dual mapping relation between $|a|<1$ and $|a|>1$ with regard to the potential tuning parameter $a$. The localization property of $|a|<1$ can be directly mapping to that of $|a|>1$, the analytical expression of the mobility edge of $|a|>1$ is therefore obtained through spectral properties of $|a|<1$. More impressive, we prove rigorously that even if the phase $θ\neq 0$ in quasiperiodic potentials, the model becomes non-$\mathcal{PT}$ symm…
We study the localization transitions for coupled one-dimensional lattices with quasiperiodic potential. Besides the localized and extended phases there is an intermediate mixed phase which can be easily explained decoupling the system so as to deal with effective uncoupled Aubry-André chains with different transition points. We clarify, therefore, the origin of such an intermediate phase finding the conditions for getting a uniquely defined mobility edge for such coupled systems. Finally we consider many coupled chains with an energy shift which compose an extension of the Aubry-André model i…
