Many-body localization (MBL) behavior is analyzed in an extended Bose-Hubbard model with quasiperiodic infinite-range interactions. No additional disorder is assumed. The analysis of the level statistics and of the eigenstates' entanglement entropy shows that a significant fraction of eigenstates becomes localized as the strength of the global interactions is increased. This behavior scales differently depending on the choice of the thermodynamic limit. The system is asymptotically ergodic by scaling the interaction strength so as to keep the energy extensive. On the other hand, the MBL regime seems to be stable if one allows for a superextensive scaling of the energy. We argue that our findings can be experimentally verified in many-body cavity quantum electrodynamics setups by means of the so-called quench spectroscopy. The latter can allow one, amongst others, to reveal the presence of a mobility edge.
Many-body localization (MBL) behavior is analyzed in an extended Bose-Hubbard model with quasiperiodic infinite-range interactions. No additional disorder is assumed. The analysis of the level statistics and of the eigenstates' entanglement entropy shows that a significant fraction of eigenstates becomes localized as the strength of the global interactions is increased. This behavior scales differently depending on the choice of the thermodynamic limit. The system is asymptotically ergodic by scaling the interaction strength so as to keep the energy extensive. On the other hand, the MBL regime seems to be stable if one allows for a superextensive scaling of the energy. We argue that our findings can be experimentally verified in many-body cavity quantum electrodynamics setups by means of the so-called quench spectroscopy. The latter can allow one, amongst others, to reveal the presence of a mobility edge.
The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from “extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to “localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder – if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using “quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.
We review the physics of many-body localization in models with incommensurate potentials. In particular, we consider one-dimensional quasiperiodic models with single-particle mobility edges. A conventional perspective suggests that delocalized states act as a thermalizing bath for the localized states in the presence of of interactions. However, contrary to this intuition there is evidence that such systems can display non-ergodicity. This is in part due to the fact that the delocalized states do not have any kind of protection due to symmetry or topology and are thus susceptible to localization. A study of such incommensurate models, in the non-interacting limit, shows that they admit extended, partially extended, and fully localized many-body states. Non-interacting incommensurate models cannot thermalize dynamically and remain localized upon the introduction of interactions. In particular, for a certain range of energy, the system can host a non-ergodic extended (i.e. metallic) phase in which the energy eigenstates violate the eigenstate thermalization hypothesis (ETH) but the entanglement entropy obeys volume-law scaling. The level statistics and entanglement growth also indicate the lack of ergodicity in these models. The phenomenon of localization and non-ergodicity in a system with interactions despite the presence of single-particle delocalized states is closely related to the so-called many-body proximity effect and can also be observed in models with disorder coupled to systems with delocalized degrees of freedom. Many-body localization in systems with incommensurate potentials (without single-particle mobility edges) have been realized experimentally, and we show how this can be modified to study the the effects of such mobility edges. Demonstrating the failure of thermalization in the presence of a single-particle mobility edge in the thermodynamic limit would indicate a more robust violation of the ETH.
We review the physics of many‐body localization in models with incommensurate potentials. In particular, we consider one‐dimensional quasiperiodic models with single‐particle mobility edges. A conventional perspective suggests that delocalized states act as a thermalizing bath for the localized states in the presence of of interactions. However, contrary to this intuition there is evidence that such systems can display non‐ergodicity. This is in part due to the fact that the delocalized states do not have any kind of protection due to symmetry or topology and are thus susceptible to localization. A study of such incommensurate models, in the non‐interacting limit, shows that they admit extended, partially extended, and fully localized many‐body states. Non‐interacting incommensurate models cannot thermalize dynamically and remain localized upon the introduction of interactions. In particular, for a certain range of energy, the system can host a non‐ergodic extended (i.e. metallic) phase in which the energy eigenstates violate the eigenstate thermalization hypothesis (ETH) but the entanglement entropy obeys volume‐law scaling. The level statistics and entanglement growth also indicate the lack of ergodicity in these models. The phenomenon of localization and non‐ergodicity in a system with interactions despite the presence of single‐particle delocalized states is closely related to the so‐called “many‐body proximity effect” and can also be observed in models with disorder coupled to systems with delocalized degrees of freedom. Many‐body localization in systems with incommensurate potentials (without single‐particle mobility edges) have been realized experimentally, and we show how this can be modified to study the the effects of such mobility edges. Demonstrating the failure of thermalization in the presence of a single‐particle mobility edge in the thermodynamic limit would indicate a more robust violation of the ETH. image
As disorder strength increases in quantum many-body systems a new phase of matter, the so-called many-body localization, emerges across the whole spectrum. This transition is energy dependent, a phenomenon known as mobility edge, such that the mid-spectrum eigenstates tend to localize at larger values of disorder in comparison to eigenstates near the edges of the spectrum. Many-body localization becomes more sophisticated in long-range interacting systems. Here, by focusing on several quantities, we draw the phase diagram as a function of disorder strength and energy spectrum, for a various range of interactions. Regardless of the underlying transition type, either second-order or Kosterlitz-Thouless, our analysis consistently determines the mobility edge, i.e., the phase boundary across the spectrum. We show that, long-range interaction enhances the localization effect and shifts the phase boundary towards smaller values of disorder. In addition, we establish a hierarchy among the studied quantities concerning their corresponding transition boundary and critical exponents. Interestingly, we show that deliberately discarding some information of the system can mitigate finite-size effects and provide results in line with the analytical predictions at the thermodynamic limit.
The localization properties of one-dimensional degenerate Fermi gases with cavity-assisted nonlocal quasiperiodic interactions are numerically studied. Although the cavity-induced interaction is typically nonlocal, it is proved that the eigenstate thermalization hypothesis is still applicable in our system depending on the system parameters. We also find the segment of the spectrum corresponding to infinite effective temperature varies for different system parameters, which indicates the spectral range employed in the spectral statistical analysis should be varied accordingly. The features of many-body localization (MBL) are numerically identified by analyzing the spectral statistics and the entanglement entropy using exact diagonalization. These features are further confirmed by our time-evolution results. In addition, the number of cavity photons are found stable over long-time dynamics in the MBL phase. Such a feature cannot only be utilized to nondestructively diagnose the MBL phase by monitoring the number of leaking photons from the cavity but leveraged for constructing a device to produce a stable number of photons.
We investigate long-range resonances in quasiperiodic many-body localized (MBL) systems. Focusing on the Heisenberg chain in a deterministic Aubry-André potential, we complement standard diagnostics by analyzing the structure of long-distance pairwise correlations at high energy. Contrary to the expectation that the ergodic-MBL transition in quasiperiodic systems should be sharper due to the absence of Griffiths regions, we uncover a broad unconventional regime at strong quasiperiodic potential, characterized by fat-tailed distributions of longitudinal correlations at long distance. This reveals the presence of atypical eigenstates with strong long-range correlations in a regime where standard diagnostics indicate stable MBL. We further identify these anomalous eigenstates as quasidegenerate pairs of resonant cat states, which exhibit entanglement at long distance. These findings advance the understanding of quasiperiodic MBL and identify density-correlation measurements in ultracold atomic systems as a probe of long-range resonances.