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Register a new userPhase diagram of a generalized off-diagonal Aubry-Andr{e} model with p-wave pairing
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Off-diagonal Aubry-Andr{e} (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.
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We study a one-dimensional quasiperiodic system described by the off-diagonal Aubry-Andr{e} model and investigate its phase diagram by using the symmetry and the multifractal analysis. It was shown in a recent work ({it Phys. Rev. B} {bf 93}, 205441 (2016)) that its phase diagram was divided into three regions, dubbed the extended, the topologically-nontrivial localized and the topologically-trivial localized phases, respectively. Out of our expectation, we find an additional region of the extended phase which can be mapped into the original one by a symmetry transformation. More unexpectedly, in both localized phases, most of the eigenfunctions are neither localized nor extended. Instead, they display critical features, that is, the minimum of the singularity spectrum is in a range $0<gamma_{min}<1$ instead of $0$ for the localized state or $1$ for the extended state. Thus, a mixed phase is found with a mixture of localized and critical eigenfunctions.
We investigate the nonequilibrium dynamics of the one-dimension Aubry-Andr{e}-Harper model with $p$-wave superconductivity by changing the potential strength with slow and sudden quench. Firstly, we study the slow quench dynamics from localized phase to critical phase by linearly decreasing the potential strength $V$. The localization length is finite and its scaling obeys the Kibble-Zurek mechanism. The results show that the second-order phase transition line shares the same critical exponent $z u$, giving the correlation length $ u=0.997$ and dynamical exponent $z=1.373$, which are different from the Aubry-Andr{e} model. Secondly, we also study the sudden quench dynamics between three different phases: localized phase, critical phase, and extended phase. In the limit of $V=0$ and $V=infty$, we analytically study the sudden quench dynamics via the Loschmidt echo. The results suggest that, if the initial state and the post-quench Hamiltonian are in different phases, the Loschmidt echo vanishes at some time intervals. Furthermore, we found that, if the initial value is in the critical phase, the direction of the quench is the same as one of the two limits mentioned before, and similar behaviors will occur.
Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge protected by a duality symmetry. These one-dimensional tight-binding models can be viewed as a generalization of the well-known Aubry-Andr{e} (AA) model, with an energy-dependent self duality condition that constitutes an analytical mobility edge relation. By adiabatically preparing the lowest and highest energy eigenstates of this model system and performing microscopic measurements of their participation ratio, we track the evolution of the mobility edge as the energy-dependent density of states is modified by the models tuning parameter. Our results show strong deviations from single-particle predictions, consistent with attractive interactions causing both enhanced localization of the lowest energy state due to self-trapping and inhibited localization of the highest energy state due to screening. This study paves the way for quantitative studies of interaction effects on self duality induced mobility edges.
We study a class of off-diagonal quasiperiodic hopping models described by one-dimensional Su-Schrieffer-Heeger chain with quasiperiodic modulations. We unveil a general dual-mapping relation in parameter space of the dimerization strength $lambda$ and the quasiperiodic modulation strength $V$, regardless of the specific details of the quasiperiodic modulation. Moreover, we demonstrated semi-analytically and numerically that under the specific quasiperiodic modulation, quantum criticality can emerge and persist in a wide parameter space. These unusual properties provides a distinctive paradigm compared with the diagonal quasiperiodic systems.
We study a non-Hermitian AA model with the long-range hopping, $1/r^a$, and different choices of the quasi-periodic parameters $beta$ to be the member of the metallic mean family. We find that when the power-law exponent is in the $a<1$ regime, the system displays a delocalized-to-multifractal (DM) edge in its eigenstate spectrum. For the $a>1$ case, it exists a delocalized-to-localized (DL) edge, also called the mobility edge. While a striking feature of the Hermitian AA model with the long-range hopping is that the fraction of delocalized states can be obtained from a general sequence manifesting a mathematical feature of the metallic mean family, we find that the DM or DL edge for the non-Hermitian cases is independent of the mathematical feature of the metallic mean family. To understand this difference, we consider a specific case of the non-Hermitian long-range AA model with $a=2$, for which we can apply the Sarnak method to analytically derive its localization transition points and the exact expression of the DL edge. Our analytical result clearly demonstrates that the mobility edge is independent of the quasi-periodic parameter $beta$, which confirms our numerical result. Finally, an optical setup is proposed to realize the non-Hermitian long-range AA model.
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