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Register a new userMany-body mobility edges in a one-dimensional model of interacting fermions
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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.
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Whether the many-body mobility edges can exist in a one-dimensional interacting quantum system is a controversial problem, mainly hampered by the limited system sizes amenable to numerical simulations. We investigate the transition from chaos to localization by constructing a combined random matrix, which has two extremes, one of Gaussian orthogonal ensemble and the other of Poisson statistics, drawn from different distributions. We find that by fixing a scaling parameter, the mobility edges can exist while increasing the matrix dimension $Drightarrowinfty$, depending on the distribution of matrix elements of the diagonal uncorrelated matrix. By applying those results to a specific one-dimensional isolated quantum system of random diagonal elements, we confirm the existence of a many-body mobility edge, connecting it with results on the onset of level repulsion extracted from ensembles of mixed random matrices.
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.
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.
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.
Many-body localization (MBL) has been widely investigated for both fermions and bosons, it is, however, much less explored for anyons. Here we numerically calculate several physical characteristics related to MBL of a one-dimensional disordered anyon-Hubbard model in both localized and delocalized regions. We figure out a logarithmically slow growth of the half-chain entanglement entropy and an area-law rather than volume-law obedience for the highly excited eigenstates in the MBL phase. The adjacent energy level gap-ratio parameter is calculated and is found to exhibit a Poisson-like probability distribution in the deep MBL phase. By studying a hybridization parameter, we reveal an intriguing effect that the statistics can induce localization-delocalization transition. Several physical quantities, such as the half-chain entanglement, the adjacent energy level gap-ratio parameter, {color{black} the long-time limit of the particle imbalance}, and the critical disorder strength, are shown to be non-monotonically dependent on the anyon statistical angle. Furthermore, a feasible scheme based on the spectroscopy of energy levels is proposed for the experimental observation of these statistically related properties.
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