Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLocalization and topological transitions in non-Hermitian quasiperiodic lattices
89
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We investigate the localization and topological transitions in a one-dimensional (interacting) non-Hermitian quasiperiodic lattice, which is described by a generalized Aubry-Andr{e}-Harper model with irrational modulations in the off-diagonal hopping and on-site potential and with non-Hermiticities from the nonreciprocal hopping and complex potential phase. For noninteracting cases, we reveal that the nonreciprocal hopping (the complex potential phase) can enlarge the delocalization (localization) region in the phase diagrams spanned by two quasiperiodical modulation strengths. We show that the localization transition are always accompanied by a topological phase transition characterized the winding numbers of eigenenergies in three different non-Hermitian cases. Moreover, we find that a real-complex eigenenergy transition in the energy spectrum coincides with (occurs before) these two phase transitions in the nonreciprocal (complex potential) case, while the real-complex transition is absent under the coexistence of the two non-Hermiticities. For interacting spinless fermions, we demonstrate that the extended phase and the many-body localized phase can be identified by the entanglement entropy of eigenstates and the level statistics of complex eigenenergies. By making the critical scaling analysis, we further show that the many-body localization transition coincides with the real-complex transition and occurs before the topological transition in the nonreciprocal case, which are absent in the complex phase case.
rate research
Read More
Time-periodic driving fields could endow a system with peculiar topological and transport features. In this work, we find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the lattice periodically. The driving force dresses the hopping amplitudes between lattice sites, yielding alternate transitions between localized, mobility edge and extended non-Hermitian quasicrystalline phases. We apply our Floquet engineering approach to five representative models of non-Hermitian quasicrystals, obtain the conditions of photon-assisted localization transitions and mobility edges, and find the expressions of Lyapunov exponents for some models. We further introduce topological winding numbers of Floquet quasienergies to distinguish non-Hermitian quasicrystalline phases with different localization nature. Our discovery thus extend the study of quasicrystals to non-Hermitian Floquet systems, and provide an efficient way of modulating the topological and transport properties of these unique phases.
Precise nature of MBL transitions in both random and quasiperiodic (QP) systems remains elusive so far. In particular, whether MBL transitions in QP and random systems belong to the same universality class or two distinct ones has not been decisively resolved. Here we investigate MBL transitions in one-dimensional ($d!=!1$) QP systems as well as in random systems by state-of-the-art real-space renormalization group (RG) calculation. Our real-space RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent $ u!approx!2.4$, which respects the Harris-Luck bound ($ u!>!1/d$) for QP systems. Note that $ u!approx! 2.4$ for QP systems also satisfies the Harris-CCFS bound ($ u!>!2/d$) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. We shall briefly discuss experimental means to measure $ u$ of QP-induced MBL transitions.
Non-Hermiticity from non-reciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization in a textit{non-reciprocal} quasiperiodic lattice, dubbed non-reciprocal Aubry-Andr{e} model, and a textit{rescaled} transition point is exactly proved. The non-reciprocity can induce not only the NHSE, but also the asymmetry in localized states with two Lyapunov exponents for both sides. Meanwhile, this transition is also topological, characterized by a winding number associated with the complex eigenenergies under periodic boundary conditions (PBCs), establishing a textit{bulk-bulk} correspondence. This interplay can be realized by an elaborately designed electronic circuit with only linear passive RLC devices instead of elusive non-reciprocal ones, where the transport of a continuous wave undergoes a transition between insulating and amplifying. This initiative scheme can be immediately applied in experiments to other non-reciprocal models, and will definitely inspires the study of interplay of NHSEs and more other quantum/topological phenomena.
Two dimensional topological superconductors (TS) host chiral Majorana modes (MMs) localized at the boundaries. In this work, within quasiclassical approximation we study the effect of disorder on the localization length of MMs in two dimensional spin-orbit (SO) coupled superconductors. We find nonmonotonic behavior of the Majorana localization length as a function of disorder strength. At weak disorder, the Majorana localization length decreases with an increasing disorder strength. Decreasing the disorder scattering time below a critical value $tau_c$, the Majorana localization length starts to increase. The critical scattering time depends on the relative magnitudes of the two ingredients behind TS: SO coupling and exchange field. For dominating SO coupling, $tau_c$ is small and vice versa for the dominating exchange field.
The boundary of a topological insulator (TI) hosts an anomaly restricting its possible phases: e.g. 3D strong and weak TIs maintain surface conductivity at any disorder if symmetry is preserved on-average, at least when electron interactions on the surface are weak. However the interplay of strong interactions and disorder with the boundary anomaly has not yet been theoretically addressed. Here we study this combination for the edge of a 2D TI and the surface of a 3D weak TI, showing how it can lead to an Anomalous Many Body Localized (AMBL) phase that preserves the anomaly. We discuss how the anomalous Kramers parity switching with pi flux arises in the bosonized theory of the localized helical state. The anomaly can be probed in localized boundaries by electrostatically sensing nonlinear hopping transport with e/2 shot noise. Our AMBL construction in 3D weak TIs fails for 3D strong TIs, suggesting that their anomaly restrictions are distinguished by strong interactions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
