Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantitative analysis of interaction effects in generalized Aubry-Andre-Harper models
119
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a quantitative analysis of two-particle interaction effects in generalized, one-dimensional Aubry-Andre-Harper models with the Fermi energy placed in one of the band gaps. We investigate systems with periodic as well as open boundary conditions; for the latter focusing on the number of edge states and the boundary charge. Both these observables are important for the classification of noninteracting topological systems. In our first class of models the unit cell structure stems from periodically modulated single-particle parameters. In the second it results from the spatial modulation of the two-particle interaction. For both types of models, we find that the single-particle band gaps are renormalized by the interaction in accordance with expectations employing general field theoretical arguments. While interaction induced effective edge states can be found in the local single-particle spectral function close to a boundary, the characteristics of the boundary charge are not modified by the interaction. This indicates that our results for the Rice-Mele and Su-Schriefer-Heeger model [Phys. Rev. B 102, 085122 (2020)] are generic and can be found in lattice models with more complex unit cells as well.
rate research
Read More
A generalization of the Aubry-Andre-Harper (AAH) model is developed, containing a tunable phase shift between on-site and off-diagonal modulations. A localization transition can be induced by varying just this phase, keeping all other model parameters constant. The complete localization phase diagram is obtained. Unlike the original AAH model, the generalized model can exhibit a transition between topologically trivial bandstructures and topologically non-trivial bandstructures containing protected boundary states. These boundary states can be pumped across the system by adiabatic variations in the phase shift parameter. The model can also be used to demonstrate the phenomenon of adiabatic pumping breakdown due to localization.
Here we study the phase diagram of the Aubry-Andre-Harper model in the presence of strong interactions as the strength of the quasiperiodic potential is varied. Previous work has established the existence of many-body localized phase at large potential strength; here, we find a rich phase diagram in the delocalized regime characterized by spin transport and unusual correlations. We calculate the non-equilibrium steady states of a boundary-driven strongly interacting Aubry-Andre-Harper model by employing the time-evolving block decimation algorithm on matrix product density operators. From these steady states, we extract spin transport as a function of system size and quasiperiodic potential strength. This data shows spin transport going from superdiffusive to subdiffusive well before the localization transition; comparing to previous results, we also find that the transport transition is distinct from a transition observed in the speed of operator growth in the model. We also investigate the correlation structure of the steady state and find an unusual oscillation pattern for intermediate values of the potential strength. The unusual spin transport and quantum correlation structure suggest multiple dynamical phases between the much-studied thermal and many-body-localized phases.
We study one-dimensional optical lattices described by generalized Aubry-Andre models that include both commensurate and incommensurate modulations of the hopping amplitude. This brings together two interesting features of this class of systems: Anderson localization and the existence of topological edge states. We follow changes of the single-particle energy spectrum induced by variations of the system parameters, with focus on the survival of topological states in the localized regime.
Non-Hermitian quantum many-body systems are a fascinating subject to be explored. Using the generalized density matrix renormalisation group method and complementary exact diagonalization, we elucidate the many-body ground states and dynamics of a 1D interacting non-Hermitian Aubry-Andre-Harper model for bosons. We find stable ground states in the superfluid and Mott insulating regimes under wide range of conditions in this model. We reveal a skin superfluid state induced by the non-Hermiticity from the nonreciprocal hopping. We investigate the topology of the Mott insulating phase and find its independence of the non-Hermiticity. The topological Mott insulators in this non-Hermitian system are characterized by four equal Chern numbers and a quantized shift of biorthogonal many-body polarizations. Furthermore, we show generic asymmetric expansion and correlation dynamics in the system.
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 give the numerical verification by calculating the inverse participation ratio and Husimi function. The exact MEs of the two models are also obtained by calculating the localization lengths and using the duality relations. Our result may provide insight into realizing and observing exact MEs in both theory and experiment.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
