Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDynamical observation of mobility edges in one-dimensional incommensurate optical lattices
111
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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. We utilize the Loschmidt echo dynamics by choosing different eigenstates as initial states and sudden changing the parameters of the system to distinguish the phases in the presence of such system.
rate research
Read More
Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate bands of localized states from bands of critical states in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite band of critical states. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order.
The mobility edges (MEs) in energy which separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic results which allow for an exact understanding are rare. Here we uncover a class of exactly solvable 1D models with MEs in the spectra, where quasiperiodic on-site potentials are inlaid in the lattice with equally spaced sites. The analytical solutions provide the exact results not only for the MEs, but also for the localization and extended features of all states in the spectra, as derived through computing the Lyapunov exponents from Avilas global theory, and also numerically verified by calculating the fractal dimension. We further propose a novel scheme with experimental feasibility to realize our model based on an optical Raman lattice, which paves the way for experimental exploration of the predicted exact ME physics.
We analyze many body localization (MBL) in an interacting one-dimensional system with a deterministic aperiodic potential. Below the threshold value of the potential $h < h_c$, the non-interacting system has single particle mobility edges at $pm E_c$ while for $ h > h_c$ all the single particle states are localized. We demonstrate that even in the presence of single particle mobility edges, the interacting system can have MBL. Our numerical calculation of participation ratio in the Fock space and Shannon entropy shows that both for $h < h_c$ (quarter filled) and $h>h_c$ ($hsim h_c$ and half filled), many body states in the middle of the spectrum are delocalized while the low energy states with $E < E_1$ and the high energy states with $E> E_2$ are localized. Variance of entanglement entropy (EE) also shows divergence at $E_{1,2}$ indicating a transition from MBL to delocalized regime. We also studied eigenstate thermalisation hypothesis (ETH) and found that the low energy many body states, which show area law scaling for EE do not obey ETH. The crossings from volume to area law scaling for EE and from thermal to non-thermal behaviour occurs deep inside the localised regime. For $h gg h_c$, all the many body states remain localized for weak to intermediate strength of interaction and the system shows infinite temperature MBL phase.
We investigate localization-delocalization transition in one-dimensional non-Hermitian quasiperiodic lattices with exponential short-range hopping, which possess parity-time ($mathcal{PT}$) symmetry. The localization transition induced by the non-Hermitian quasiperiodic potential is found to occur at the $mathcal{PT}$-symmetry-breaking point. Our results also demonstrate the existence of energy dependent mobility edges, which separate the extended states from localized states and are only associated with the real part of eigen-energies. The level statistics and Loschmidt echo dynamics are also studied.
We investigate the dynamical evolution of a parity-time ($mathcal{PT}$) symmetric extension of the Aubry-Andr{e} (AA) model, which exhibits the coincidence of a localization-delocalization transition point with a $mathcal{PT}$ symmetry breaking point. One can apply the evolution of the profile of the wave packet and the long-time survival probability to distinguish the localization regimes in the $mathcal{PT}$ symmetric AA model. The results of the mean displacement show that when the system is in the $mathcal{PT}$ symmetry unbroken regime, the wave-packet spreading is ballistic, which is different from that in the $mathcal{PT}$ symmetry broken regime. Furthermore, we discuss the distinctive features of the Loschmidt echo with the post-quench parameter being localized in different $mathcal{PT}$ symmetric regimes.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
