We theoretically study a one-dimensional (1D) mutually incommensurate bichromatic lattice system which has been implemented in ultracold atoms to study quantum localization. It has been universally believed that the tight-binding version of this bichromatic incommensurate system is represented by the well-known Aubry-Andre model. Here we establish that this belief is incorrect and that the Aubry-Andre model description, which applies only in the extreme tight-binding limit of very deep primary lattice potential, generically breaks down near the localization transition due to the unavoidable appearance of single-particle mobility edges (SPME). In fact, we show that the 1D bichromatic incommensurate potential system manifests generic mobility edges which disappear in the tight-binding limit, leading to the well-studied Aubry-Andre physics. We carry out an extensive study of the localization properties of the 1D incommensurate optical lattice without making any tight-binding approximation. We find that, for the full lattice system, an intermediate phase between completely localized and completely delocalized regions appears due to the existence of the SPME, making the system qualitatively distinct from the Aubry-Andre prediction. Using the Wegner flow approach, we show that the SPME in the real lattice system can be attributed to significant corrections of higher-order harmonics in the lattice potential which are absent in the strict tight-binding limit. We calculate the dynamical consequences of the intermediate phase in detail to guide future experimental investigations for the observation of 1D SPME and the associated intermediate phase. We consider effects of interaction numerically, and conjecture the stability of SPME to weak interaction effects, thus leading to the exciting possibility of an experimentally viable nonergodic extended phase in interacting 1D optical lattices.
We investigate the interplay between disorder and superconducting pairing for a one-dimensional $p$-wave superconductor subject to slowly varying incommensurate potentials with mobility edges. With amplitude increments of the incommensurate potentials, the system can undergo a transition from a topological phase to a topologically trivial localized phase. Interestingly, we find that there are four mobility edges in the spectrum when the strength of the incommensurate potential is below a critical threshold, and a novel topologically nontrivial localized phase emerges in a certain region. We re…
Localization properties of non-interacting quantum particles in one-dimensional incommensurate lattices are investigated with an exponential short-range hopping that is beyond the minimal nearest-neighbor tight-binding model. Energy dependent mobility edges are analytically predicted in this model and verified with numerical calculations. The results are then mapped to the continuum Schrodinger equation, and an approximate analytical expression for the localization phase diagram and the energy dependent mobility edges in the ground band obtained.
We investigate the wave packet dynamics for a one-dimensional incommensurate optical lattice with a special on-site potential which exhibits the mobility edge in a compactly analytic form. We calculate the density propagation, long-time survival probability and mean square displacement of the wave packet in the regime with the mobility edge and compare with the cases in extended, localized and multifractal regimes. Our numerical results indicate that the dynamics in the mobility-edge regime mix both extended and localized features which is quite different from that in the mulitfractal phase. W…
In this paper, we look at four generalizations of the one dimensional Aubry-Andre-Harper (AAH) model which possess mobility edges. We map out a phase diagram in terms of population imbalance, and look at the system size dependence of the steady state imbalance. We find non-monotonic behaviour of imbalance with system parameters, which contradicts the idea that the relaxation of an initial imbalance is fixed only by the ratio of number of extended states to number of localized states. We propose that there exists dimensionless parameters, which depend on the fraction of single particle localize…
We study theoretically the localization properties of two distinct one-dimensional quasiperiodic lattice models with a single-particle mobility edge (SPME) separating extended and localized states in the energy spectrum. The first one is the familiar Soukoulis-Economou trichromatic potential model with two incommensurate potentials, and the second is a system consisting of two coupled 1D Aubry-Andre chains each containing one incommensurate potential. We show that as a function of the Hamiltonian model parameters, both models have a wide single-particle intermediate phase (SPIP), defined as th…
Off-diagonal Aubry-André (AA) model has recently attracted a great deal of attention as they provide condensed matter realization of topological phases. We numerically study a generalized off-diagonal AA model with p-wave superfluid pairing in the presence of both commensurate and incommensurate hopping modulations. The phase diagram as functions of the modulation strength of incommensurate hopping and the strength of the p-wave pairing is obtained by using the multifractal analysis. We show that with the appearance of the p-wave pairing, the system exhibits mobility-edge phases and critical p…
We study many-body localization (MBL) in the quasiperiodic $t_1$-$t_2$ model, focusing on the role of next-nearest-neighbor (NNN) hopping $t_2$, which introduces a single-particle mobility edge. The calculated phase diagram can be divided into three distinct regimes, depending on the strength of the short-range interaction $U$. For weak interactions ($U\ll t_1$), this model is always nonthermal. For intermediate interactions ($U\sim t_1$), the thermal-MBL phase transition in this model is qualitatively the same as that of the Aubry-Andre (AA) model, which is consistent with existing experiment…
Conventionally the mobility edge (ME) separating extended states from localized ones is a central concept in understanding Anderson localization transition. The critical state, being delocalized and non-ergodic, is a third type of fundamental state that is different from both the extended and localized states. Here we study the localization phenomena in a one dimensional periodically kicked quasiperiodic optical Raman lattice by using fractal dimensions. We show a rich phase diagram including the pure extended, critical and localized phases in the high frequency regime, the MEs separating the …
We study the one-dimensional tight-binding models which include a slowly varying, incommensurate off-diagonal modulation on the hopping amplitude. Interestingly, we find that the mobility edges can appear only when this off-diagonal (hopping) disorder is included in the model, which is different from the known results induced by the diagonal disorder. We further study the situation where the off-diagonal and diagonal disorder terms (the incommensurate potential) are both included and find that the locations of mobility edges change significantly and the varying trend of the mobility edge becom…
Topological phonon polaritons (TPhPs) are promising optical modes relevant in long-range radiative heat transfer, information processing and infrared sensing, whose topological protection is expected to enable their robust existence and transport. In this work we show that TPhPs can be supported in one-dimensional (1D) bichromatic silicon carbide nanoparticle (NP) chains, and demonstrate that they can considerably enhance radiative heat transfer for an array much longer than the wavelength of radiation. By introducing incommensurate or commensurate modulations on the interparticle distances, t…
We study a one-dimensional quasiperiodic system described by the Aubry-André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry-André model are either extended or localized depending on the strength of incommensurate potential $V$ being less or bigger than a critical value $V_c$, and thus no mobility edge exists. However, it was shown in a recent work that this conclusion does not hold true when the wave vector $α$ of the incommensurate potential is small, and for the…
Single particle localization of an ultra-cold atom is studied in one dimension when the atom is confined by an optical lattice and by the incommensurate potential of a high-finesse optical cavity. In the strong coupling regime the atom is a dynamical refractive medium, the cavity resonance depends on the atomic position within the standing-wave mode and nonlinearly determines the depth and form of the incommensurate potential. We show that the particular form of the quasi-random cavity potential leads to the appearance of mobility edges, even in presence of nearest-neighbour hopping. We provid…
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 study a one-dimensional system that includes both a commensurate off-diagonal modulation of the hopping amplitude and an incommensurate, slowly varying diagonal on-site modulation. By using asymptotic heuristic arguments, we identify four closed form expressions for the mobility edges. We further study numerically the inverse participation ratio, the density of states and the Lyapunov exponent. The numerical results are in exact agreement with our theoretical predictions. Besides a metal-insulator transition driven by the strength of the slowly varying potential, another four insulator-meta…
We study superconductivity in a family of one dimensional incommensurate system with $s$-wave pairing interaction. The incommensurate potential can alter the spatial characteristics of electrons in the normal state, leading to either extended, critical, or localized wave functions. We find that superconductivity is significantly enhanced when the electronic wave function exhibits a critical multifractal structure. This criticality also manifests itself in the power-law dependence of superconducting temperature on the pairing strength. As a consequence, an extended superconducting domain is exp…
Steady-state thermoelectric machines convert heat into work by driving a thermally-generated charge current against a voltage gradient. In this work, we propose a new class of steady-state heat engines operating in the quantum regime, where a quasi-periodic tight-binding model that features a mobility edge forms the working medium. In particular, we focus on a generalization of the paradigmatic Aubrey-André-Harper (AAH) model, known to display a single-particle mobility edge that separates the energy spectrum into regions of completely delocalized and localized eigenstates. Remarkably, these t…
In non-Hermitian quasicrystals, mobility edges (ME) separating localized and extended states in complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. Such ME are of topological nature, i.e. the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. However, depending on the origin of non-Hermiticity, i.e. asymmetry of hopping amplitudes or complexification of the incommensurate potential phase, different winding numbers are introduced, corresponding to different transport features in the bulk of the lattice…
A mobility edge (ME) in energy separating extended from localized states is a central concept in understanding various fundamental phenomena like the metal-insulator transition in disordered systems. In one-dimensional quasiperiodic systems, there exist a few models with exact MEs, and these models are beneficial to provide exact understanding of ME physics. Here we investigate two widely studied models including exact MEs, one with an exponential hopping and one with a special form of incommensurate on-site potential. We analytically prove that the two models are mutually dual, and further gi…
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）
We discuss a two-dimensional system under the perturbation of a Moire potential, which takes the same geometry and lattice constant as the underlying lattices but mismatches up to relative rotation. Such a self-dual model belongs to the orthogonal class of a quasi-periodic system whose features have been evasive in previous studies. We find that such systems enjoy the same scaling exponent as the one-dimensional Aubry-Andre model $ ν\approx 1 $, which saturates the Harris bound $ ν>2/d=1 $ in two-dimensions. Meanwhile, there exist an infinite number of mobility edges different from the typical…
We study the dynamic structure factor of a one-dimensional Bose gas confined in an optical lattice and modeled by the Bose-Hubbard Hamiltonian, using a variety of numerical and analytical approaches. The dynamic structure factor, experimentally measurable by Bragg spectroscopy, is studied in three relevant cases: in the clean regime, featuring either a superfluid or a Mott phase; and in the presence of two types of (quasi-)disordered external potentials: a quasi-periodic potential obtained from a bichromatic superlattice and a random-box disorder - both featuring a Bose glass phase. In the cle…
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）
We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We investigate incommensurate lattices and random disorder Anderson models. Many-body localization and quantum nonergodic properties are studied by comparing entanglement and thermal entropy, and by calculating the scaling of subsystem particle number fluctuations, respectively. We establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of non-interacting fermions where the e…
We study the quantum localization phenomena of noninteracting particles in one-dimensional lattices based on tight-binding models with various forms of hopping terms beyond the nearest neighbor, which are generalizations of the famous Aubry-André and noninteracting Anderson model. For the case with deterministic disordered potential induced by a secondary incommensurate lattice (i.e. the Aubry-André model), we identify a class of self dual models, for which the boundary between localized and extended eigenstates are determined analytically by employing a generalized Aubry-André transformation.…
