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arXiv:1705.03783 · Journal of Physics B Atomic Molecular and Optical Physics

Phase diagram of a generalized off-diagonal Aubry–André model with p -wave pairing

Tong Liu, Pei Wang, Shu Chen, Gao Xianlong

Published Nov 7, 2017• 15 citations
arXivHTMLPDF

Abstract

Abstract 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 phases with various number of topologically-protected zero-energy modes. Predicted topological nature of these exotic phases can be realized in a cold atomic system of incommensurate bichromatic optical lattice with induced p -wave superfluid pairing by using a Raman laser in proximity to a molecular Bose–Einstein condensation.

DOI
10.1088/1361-6455/aa98d6

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Abstract 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 phases with various number of topologically-protected zero-energy modes. Predicted topological nature of these exotic phases can be realized in a cold atomic system of incommensurate bichromatic optical lattice with induced p -wave superfluid pairing by using a Raman laser in proximity to a molecular Bose–Einstein condensation.
Using exact numerical methods, we study the interplay between p-wave superconductivity and off-diagonal modulation in the incommensurate off-diagonal Aubry-André model with p-wave pairing. When chemical potential is zero, the modulation not only leads to an Anderson-like localization with all bulk states changing into critical ones, but also induces a topological phase transition accompanying the disappearing of exponentially localized zero-energy edge Majorana fermions. These two transitions happen at different places and true Anderson localization is absent. With a finite chemical potential, the quasi-periodicity of the modulation causes band splitting and drives the system into a band insulator phase. It has a fixed incommensurate particle density which is determined by the modulation frequency. Phase diagrams are identified, and can be tested with existing proposals for experimental realizations of the effective off-diagonal disorder and the p-wave pairing.
We chart out the phases of ultracold ``spin-half'' bosons in a one-dimensional optical lattice in the presence of Aubry-Andr\'e (AA) potential and with spin-orbit (SO) and Raman couplings. We investigate the superfluid (SF) and localized phases and demonstrate the existence of density wave phase for nearest-neighbor interaction (NNI) between the bosons. We show that the presence of SO coupling and AA potential leads to a spin-split momentum distribution of the bosons in the localized phase near the boundary with the SF phase, which can act as a signature of the SF-localized phase transition. We also obtain the level statistics of the bosons in the superfluid phase with finite NNI and demonstrate its change from Gaussian unitary ensemble (GUE) to Gaussian orthogonal ensemble (GOE) as a function of the Raman coupling. We discuss experiments which can test our theory.
We analyze topological properties of the one-dimensional Bose-Hubbard model with a quasiperiodic superlattice potential. This system can be realized in interacting ultracold bosons in optical lattice in the presence of an incommensurate superlattice potential. We first analyze the quasiperiodic superlattice made by the cosine function, which we call Harper-like Bose-Hubbard model. We compute the Chern number and observe a gap-closing behavior as the interaction strength UUU is changed. Also, we discuss the bulk-edge correspondence in our system. Furthermore, we explore the phase diagram as a function of UUU and a continuous deformation parameter βββ between the Harper-like model and another important quasiperiodic lattice, the Fibonacci model. We numerically confirm that the incommensurate charge density wave (ICDW) phase is topologically non-trivial and it is topologically equivalent in the whole ICDW region.
Abstract We systematically investigate the ground state phase diagram and the finite temperature phase transitions for a Rydberg-dressed Fermi gas loaded in a bilayer optical lattice. When an effective finite-ranged attraction is induced, our self-consistent mean-field calculation shows that the gapped topological (p-wave) superfluids in each layer are coupled together by the s-wave pairing in an intermediate inter-layer distance with a spontaneously modulated phases between these two order parameters. The obtained ground state is a gapless topological superfluid with quantized topological charges characterizing the gapless points, leading to a zero energy flat band at the edges. Finally, we calculate the finite temperature phase diagrams of this two-dimensional gapless superfluid and observe two distinct critical temperatures, demonstrating the fruitful many-body effects on a paired topological superfluids.
Abstract We study the ground state phases of interacting bosons in the presence of a 2D Aubry–André (AA) potential. By using a mean-field percolation analysis, we focus on several superlattice and quasicrystalline regimes of the 2D AA model, including generalisations that account for a tilting or skewing of the potential. We show that barriers to the onset of macroscopic phases naturally arise from weakly modulated domains in the 2D AA model. This leads to the formation of extended crossover domains, in which the macroscopic properties are dominated by a minority of the system. The phase diagrams then exhibit substantially different features when compared against crystalline systems, including a lobe-like or wave-like appearance of the Bose glass, sharp extrusions and thin, percolating clusters. By studying the 2D AA model across multiple regimes, we have shown that these extended crossover domains are not distinct to a small set of parameters.
We investigate the one-dimensional longer-range Kitaev chain with an on-site complex Aubry-Andr\'e-Harper (AAH) potential. For the incommensurate (commensurate) case, by calculating the real-space (Bloch) winding number and energy spectrum we discover the AAH potential-induced phases and present the related phase diagrams. We also find that the imaginary phase shift in AAH potentials can suppress these topological phases for both cases. For the incommensurate case, the inverse participate ratios of the eigenstates with the smallest ∣E∣s|E|\mathrm{s}∣E∣s indicate the existence of the incommensurate AAH potential-induced phases, and the result of the mean inverse participate ratio shows that these incommensurate AAH potential-induced phases are not always strongly localized.