Condensed Matter

We examine the transport of magnetic energy in a simplified model of a magnetic metamaterial, consisting of a one-dimensional array of split-ring resonators, in the presence of correlated disorder in the resonant frequencies. The computation of the average participation ratio (PR) reveals that on average, the modes for the correlated disorder system are less localized than in the uncorrelated case. The numerical computation of the mean square displacement of an initially localized magnetic excitation for the correlated case shows a substantial departure from the uncorrelated (Anderson-like) case. A long-time asymptotic fit ⟨ n 2 ⟩∼ t α reveals that, for the uncorrelated system α∼0 , while for the correlated case α>0 , spanning a whole range of behavior ranging from localization to super-diffusive behavior. The transmission coefficient of a plane wave across a single magnetic dimer reveals the existence of well-defined regions in disorder strength-magnetic coupling space, where unit transmission for some wavevector(s) is possible. This implies, according to the random dimer model (RDM) of Dunlap et al., a degree of mobility. A comparison between the mobilities of the correlated SRR system and the RDM shows that the RDM model has better mobility at low disorder while our correlated SRR model displays better mobility at medium and large disorder.

We study the full many-body localization (MBL) in the Rydberg atomic quantum simulator with quasiperiodic modulation. Employing both exact diagonalization (ED) and time-evolving block decimation (TEBD) methods, we identify evidence of a constrained many-body-localized phase stabilized by a pure quasirandom field transverse to the direction of the projection. Intriguingly, through the lens of quantum dynamics, we find that rotating the modulated field from parallel towards perpendicular to the projection axis induces an eigenstate transition between the diagonal and the constrained MBL phases. Remarkably, the growth of the entanglement entropy in constrained MBL follows a double-logarithmic form, whereas it changes to a power law in the diagonal limit. Although the diagonal MBL steered by a strong modulation along the projection direction can be understood by extending the phenomenology of local integrals of motion, a thorough analysis of the constrained MBL calls for the new ingredients. As a preliminary first step, we unveil the significance of confined nonlocal effects in the integrals of motion of the constrained MBL phase, which potentially challenges the established framework of the unconstrained MBL. Since the quasiperiodic modulation has been achievable in cold-atom laboratories, the constrained and diagonal MBL regimes, as well as the eigenstate transition between them, should be within reach of the ongoing Rydberg experiments.

We study the transitions between ergodic and many-body localized phases in spin systems, subject to quenched disorder, including the Heisenberg chain and the central spin model. In both cases systems with common spin lengths 1/2 and 1 are investigated via exact numerical diagonalization and random matrix techniques. Particular attention is paid to the sample-to-sample variance ( Δ s r ) 2 of the averaged consecutive-gap ratio ⟨r⟩ for different disorder realizations. For both types of systems and spin lengths we find a maximum in Δ s r as a function of disorder strength, accompanied by an inflection point of ⟨r⟩ , signaling the transition from ergodicity to many-body localization. The critical disorder strength is found to be somewhat smaller than the values reported in the recent literature. Further information about the transitions can be gained from the probability distribution of expectation values within a given disorder realization.

Many-body localization (MBL) provides a mechanism to avoid thermalization in many-body quantum systems. Here, we show that an {\it emergent} symmetry can protect a state from MBL. Specifically, we propose a $\Z_2$ symmetric model with nonlocal interactions, which has an analytically known, SU(2) invariant, critical ground state. At large disorder strength all states at finite energy density are in a glassy MBL phase, while the lowest energy states are not. These do, however, localize when a perturbation destroys the emergent SU(2) symmetry. The model also provides an example of MBL in the presence of nonlocal, disordered interactions that are more structured than a power law. The presented ideas raise the possibility of an `inverted quantum scar', in which a state that does not exhibit area law entanglement is embedded in an MBL spectrum, which does.

Motivated by recent experiments on interacting bosons in quasi-one-dimensional optical lattice [Nature {\bf 573}, 385 (2019)] we analyse theoretically properties of the system in the crossover between delocalized and localized regimes. Comparison of time dynamics for uniform and density wave like initial states enables demonstration of the existence of the mobility edge. To this end we define a new observable, the mean speed of transport at long times. It gives us an efficient estimate of the critical disorder for the crossover. We also show that the mean velocity growth of occupation fluctuations close to the edges of the system carries the similar information. Using the quantum quench procedure we show that it is possible to probe the mobility edge for different energies.

We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than the full Hilbert space, but still exponentially. Such a property allows us to study the MBL phase transition in systems including more than 50 spins. The different Krylov spaces that we consider show clear signatures of a many-body localization transition, both in the Kullback-Leibler divergence of the distribution of their level spacing ratio and their entanglement properties. But they also present distinct scalings with system size. Depending on the subspace, the critical disorder strength can be nearly independent of the system size or conversely show an approximately linear increase with the number of spins.

In the present study, the interplay among interaction, topology, quasiperiodicity, and non-Hermiticity is studied. The hard-core bosons model on a one-dimensional lattice with asymmetry hoppings and quasiperiodic onsite potentials is selected. This model, which preserves time-reversal symmetry (TRS), will exhibit three types of phase transition: real-complex transition of eigenenergies, topological phase transition and many-body localization (MBL) phase transition. For thereal-complex transition, it is found that the imaginary parts of the eigenenergies are always suppressed by the MBL. Moreover, by calculating the winding number, a topological phase transition can be revealed with the increase of potential amplitude, and we find that the behavior is quite different from the single-particle systems. Based on our numerical results, we conjecture that these three types of phase transition occur at the same point in the thermodynamic limit, and the MBL transition of quasiperiodic system and disordered system should belong to different universality classes. Finally, we demonstrate that these phase transitions can profoundly affect the dynamics of the non-Hermitian many-body system.

Recent developments in matrix-product-state (MPS) investigations of many-body localization (MBL) are reviewed, with a discussion of benefits and limitations of the method. This approach allows one to explore the physics around the MBL transition in systems much larger than those accessible to exact diagonalization. System sizes and length scales that can be controllably accessed by the MPS approach are comparable to those studied in state-of-the-art experiments. Results for 1D, quasi-1D, and 2D random systems, as well as 1D quasi-periodic systems are presented. On time scales explored (up to t??00 in units set by the hopping amplitude), a slow, subdiffusive transport in a rather broad disorder range on the ergodic side of the MBL transition is found. For 1D random spin chains, which serve as a "standard model" of the MBL transition, the MPS study demonstrates a substantial drift of the critical point W c (L) with the system size L : while for L??0 we find W c ?? , as also given by exact diagonalization, the MPS results for L=50 --100 provide evidence that the critical disorder saturates, in the large- L limit, at W c ??.5 . For quasi-periodic systems, these finite-size effects are much weaker, which suggests that they can be largely attributed to rare events. For quasi-1D ( d?L , with d?�L ) and 2D ( L?L ) random systems, the MPS data demonstrate an unbounded growth of W c in the limit of large d and L , in agreement with analytical predictions based on the rare-event avalanche theory.

The many-body localization transition for Heisenberg spin chain with a speckle disorder is studied. Such a model is equivalent to a system of spinless fermions in an optical lattice with an additional speckle field. Our numerical results show that the many-body localization transition in speckle disorder falls within the same universality class as the transition in an uncorrelated random disorder, in contrast to the quasiperiodic potential typically studied in experiments. This hints at possibilities of experimental studies of the role of rare Griffiths regions and of the interplay of ergodic and localized grains at the many-body localization transition. Moreover, the speckle potential allows one to study the role of correlations in disorder on the transition. We study both spectral and dynamical properties of the system focusing on observables that are sensitive to the disorder type and its correlations. In particular, distributions of local imbalance at long times provide an experimentally available tool that reveals the presence of small ergodic grains even deep in the many-body localized phase in a correlated speckle disorder.

We study effects of disorder on eigenstates of 1D two-component fermions with infinitely strong Hubbard repulsion. We demonstrate that the spin-independent (potential) disorder reduces the problem to the one-particle Anderson localization taking place at arbitrarily weak disorder. In contrast, a random magnetic field can cause reentrant many-body localization-delocalization transitions. Surprisingly weak magnetic field destroys one-particle localization caused by not too strong potential disorder, whereas at much stronger fields the states are many-body localized. We present numerical support of these conclusions.