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Register a new userInvariable mobility edge in a quasiperiodic lattice
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In this paper, we study a one-dimensional tight-binding model with tunable incommensurate potentials. Through the analysis of the inverse participation rate, we uncover that the wave functions corresponding to the energies of the system exhibit different properties. There exists a critical energy under which the wave functions corresponding to all energies are extended. On the contrary, the wave functions corresponding to all energies above the critical energy are localized. However, we are surprised to find that the critical energy is a constant independent of the potentials. We use the self-dual relation to solve the critical energy, namely the mobility edge, and then we verify the analytical results again by analyzing the spatial distributions of the wave functions. Finally, we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.
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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.
Many interesting experimental systems, such as cavity QED or central spin models, involve global coupling to a single harmonic mode. Out-of-equilibrium, it remains unclear under what conditions localized phases survive such global coupling. We study energy-dependent localization in the disordered Ising model with transverse and longitudinal fields coupled globally to a $d$-level system (qudit). Strikingly, we discover an inverted mobility edge, where high energy states are localized while low energy states are delocalized. Our results are supported by shift-and-invert eigenstate targeting and Krylov time evolution up to $L=13$ and $18$ respectively. We argue for a critical energy of the localization phase transition which scales as $E_c propto L^{1/2}$, consistent with finite size numerics. We also show evidence for a reentrant MBL phase at even lower energies despite the presence of strong effects of the central mode in this regime. Similar results should occur in the central spin-$S$ problem at large $S$ and in certain models of cavity QED.
Thermalization of random-field Heisenberg spin chain is probed by time evolution of density correlation functions. Studying the impacts of average energies of initial product states on dynamics of the system, we provide arguments in favor of the existence of a mobility edge in the large system-size limit.
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.
Sufficient disorder is believed to localize static and periodically-driven interacting chains. With quasiperiodic driving by $D$ incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for $D=2$, but not for $D geq 3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D geq 3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically-driven setting, and verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.
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