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Register a new userDelocalization of weakly interacting bosons in a 1D quasiperiodic potential
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We consider weakly interacting bosons in a 1D quasiperiodic potential (Aubry-Azbel-Harper model) in the regime where all single-particle states are localized. We show that the interparticle interaction may lead to the many-body delocalization and we obtain the finite-temperature phase diagram. Counterintuitively, in a wide range of parameters the delocalization requires stronger cou- pling as the temperature increases. This means that the system of bosons can undergo a transition from a fluid to insulator (glass) state under heating.
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We study the localization properties of weakly interacting Bose gas in a quasiperiodic potential commonly known as Aubry-Andre model. Effect of interaction on localization is investigated by computing the `superfluid fraction and `inverse participation ratio. For interacting Bosons the inverse participation ratio increases very slowly after the localization transition due to `multisite localization of the wave function. We also study the localization in Aubry-Andre model using an alternative approach of classical dynamical map, where the localization is manifested by chaotic classical dynamics. For weakly interacting Bose gas, Bogoliubov quasiparticle spectrum and condensate fraction are calculated in order to study the loss of coherence with increasing disorder strength. Finally we discuss the effect of trapping potential on localization of matter wave.
Conduction through materials crucially depends on how ordered they are. Periodically ordered systems exhibit extended Bloch waves that generate metallic bands, whereas disorder is known to limit conduction and localize the motion of particles in a medium. In this context, quasiperiodic systems, which are neither periodic nor disordered, reveal exotic conduction properties, self-similar wavefunctions, and critical phenomena. Here, we explore the localization properties of waves in a novel family of quasiperiodic chains obtained when continuously interpolating between two paradigmatic limits: the Aubry-Andre model, famous for its metal-to-insulator transition, and the Fibonacci chain, known for its critical nature. Using both theoretical analysis and experiments on cavity-polariton devices, we discover that the Aubry-Andre model evolves into criticality through a cascade of band-selective localization/delocalization transitions that iteratively shape the self-similar critical wavefunctions of the Fibonacci chain. Our findings offer (i) a unique new insight into understanding the criticality of quasiperiodic chains, (ii) a controllable knob by which to engineer band-selective pass filters, and (iii) a versatile experimental platform with which to further study the interplay of many-body interactions and dissipation in a wide range of quasiperiodic models.
We consider the many-body localization-delocalization transition for strongly interacting one- dimensional disordered bosons and construct the full picture of finite temperature behavior of this system. This picture shows two insulator-fluid transitions at any finite temperature when varying the interaction strength. At weak interactions an increase in the interaction strength leads to insulator->fluid transition, and for large interactions one has a reentrance to the insulator regime.
We find that quasiperiodicity-induced localization-delocalization transitions in generic 1D systems are associated with hidden dualities that generalize the well-known duality of the Aubry-Andre model. For a given energy window, such duality is locally defined near the transition and can be explicitly determined by considering commensurate approximants. This relies on the construction of an auxiliary 2D Fermi surface of the commensurate approximants as a function of the phase-twisting boundary condition and of the phase-shifting real-space structure. Considering widely different families of quasiperiodic 1D models, we show that, around the critical point of the limiting quasiperiodic system, the auxiliary Fermi surface of a high-enough-order approximant converges to a universal form. This allows us to devise a highly-accurate method to compute mobility edges and duality transformations for generic 1D quasiperiodic systems through their commensurate approximants. To illustrate the power of this approach, we consider several previously studied systems, including generalized Aubry-Andre models and coupled Moire chains. Our findings bring a new perspective to examine quasiperiodicity-induced localization-delocalization transitions in 1D, provide a working criterion for the appearance of mobility edges, and an explicit way to understand the properties of eigenstates close and at the transition.
It is commonly accepted that there are no phase transitions in one-dimensional (1D) systems at a finite temperature, because long-range correlations are destroyed by thermal fluctuations. Here we demonstrate that the 1D gas of short-range interacting bosons in the presence of disorder can undergo a finite temperature phase transition between two distinct states: fluid and insulator. None of these states has long-range spatial correlations, but this is a true albeit non-conventional phase transition because transport properties are singular at the transition point. In the fluid phase the mass transport is possible, whereas in the insulator phase it is completely blocked even at finite temperatures. We thus reveal how the interaction between disordered bosons influences their Anderson localization. This key question, first raised for electrons in solids, is now crucial for the studies of atomic bosons where recent experiments have demonstrated Anderson localization in expanding very dilute quasi-1D clouds.
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