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Register a new userStatistically related many-body localization in the one-dimensional anyon Hubbard model
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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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Thermalizing quantum systems are conventionally described by statistical mechanics at equilibrium. However, not all systems fall into this category, with many body localization providing a generic mechanism for thermalization to fail in strongly disordered systems. Many-body localized (MBL) systems remain perfect insulators at non-zero temperature, which do not thermalize and therefore cannot be described using statistical mechanics. In this Colloquium we review recent theoretical and experimental advances in studies of MBL systems, focusing on the new perspective provided by entanglement and non-equilibrium experimental probes such as quantum quenches. Theoretically, MBL systems exhibit a new kind of robust integrability: an extensive set of quasi-local integrals of motion emerges, which provides an intuitive explanation of the breakdown of thermalization. A description based on quasi-local integrals of motion is used to predict dynamical properties of MBL systems, such as the spreading of quantum entanglement, the behavior of local observables, and the response to external dissipative processes. Furthermore, MBL systems can exhibit eigenstate transitions and quantum orders forbidden in thermodynamic equilibrium. We outline the current theoretical understanding of the quantum-to-classical transition between many-body localized and ergodic phases, and anomalous transport in the vicinity of that transition. Experimentally, synthetic quantum systems, which are well-isolated from an external thermal reservoir, provide natural platforms for realizing the MBL phase. We review recent experiments with ultracold atoms, trapped ions, superconducting qubits, and quantum materials, in which different signatures of many-body localization have been observed. We conclude by listing outstanding challenges and promising future research directions.
While many-body localization (MBL) is a well-established phenomenon in one-dimension, the fate of higher-dimensional strongly disordered systems in the infinite-time limit is a topic of current debate. The latest experiments as well as several recent numerical studies indicate that such systems behave many-body localized -- at least on practically relevant time scales. However, thus far, theoretical approaches have been unable to quantitatively reproduce experimentally measured MBL-to-thermal transition points, an important requirement to demonstrate their validity. Here, we develop a formalism to apply fermionic quantum circuits combined with automatic differentiation to simulate two-dimensional MBL systems realized in optical lattice experiments with fermions. Using entanglement-based features, we obtain a phase transition point in excellent agreement with the experimentally measured value. We argue that our approach best captures the underlying charge-density-wave experiments and calculate other quantities which can be compared to future experiments, such as the mean localization lengths.
Lessons from Anderson localization highlight the importance of dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focussed on the phenomenon in one dimension using techniques of exact diagonalization and tensor networks. On the other hand, experiments in two dimensions have provided concrete results going beyond the previously numerically accessible limits while posing several challenging questions. We present the first large-scale numerical examination of a disordered Bose-Hubbard model in two dimensions realized in cold atoms, which shows entanglement based signatures of many-body localization. By generalizing a low-depth quantum circuit to two dimensions we approximate eigenstates in the experimental parameter regimes for large systems, which is beyond the scope of exact diagonalization. A careful analysis of the eigenstate entanglement structure provides an indication of the putative phase transition marked by a peak in the fluctuations of entanglement entropy in a parameter range consistent with experiments.
We investigate the localization properties of a spin chain with an antiferromagnetic nearest-neighbour coupling, subject to an external quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates between two paradigmatic models, namely the Aubry-Andre and the Fibonacci models. We find that stronger many-body interactions extend the ergodic phase in the former, whereas they shrink it in the latter. Furthermore, the many-body localization transition points at the two limits of the interpolation appear to be continuously connected along the deformation. As a result, the position of the many-body localization transition depends on the interaction strength for an intermediate degree of deformation of the quasiperiodic modulation. Moreover, in the region of parameter space where the single-particle spectrum contains both localized and extended states, many-body interactions induce an anomalous effect: weak interactions localize the system, whereas stronger interactions enhance ergodicity. We map the models localization phase diagram using the decay of the quenched spin imbalance in relatively long chains. This is accomplished employing a time-dependent variational approach applied to a matrix product state decomposition of the many-body state. Our model serves as a rich playground for testing many-body localization under tunable potentials.
It is typically assumed that disorder is essential to realize Anderson localization. Recently, a number of proposals have suggested that an interacting, translation invariant system can also exhibit localization. We examine these claims in the context of a one-dimensional spin ladder. At intermediate time scales, we find slow growth of entanglement entropy consistent with the phenomenology of many-body localization. However, at longer times, all finite wavelength spin polarizations decay in a finite time, independent of system size. We identify a single length scale which parametrically controls both the eventual spin transport times and the divergence of the susceptibility to spin glass ordering. We dub this long pre-thermal dynamical behavior, intermediate between full localization and diffusion, quasi-many body localization.
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