Models of many-body localization (MBL) can be represented as tight-binding models in the many-body Hilbert space (Fock space). We explore the role of correlations between matrix elements of the effective Fock-space Hamiltonians in the scaling of MBL critical disorder
Wc(n) with the size
n of the system. For this purpose, we consider five models, which all have the same distributions of diagonal (energy) and off-diagonal (``hopping'') Fock-space matrix elements but different Fock-space correlations. These include quantum-dot (QD) and one-dimensional (1D) MBL models, their modifications (uQD and u1D models) with removed correlations of off-diagonal matrix elements, as well a quantum random energy model (QREM) with no correlations at all. Our numerical results are in full consistency with analytical arguments predicting ${n}^{3/4}{(lnn)}^{\ensuremath{-}1/4}\ensuremath{\lesssim}{W}_{c}\ensuremath{\lesssim}nlnn$ for the scaling of
Wc(n) in the QD model (we find ${W}_{c}\ensuremath{\sim}n$ numerically), ${W}_{c}(n)\ensuremath{\sim}\text{const}$ for the 1D model, ${W}_{c}\ensuremath{\sim}nlnn$ for the uQD and u1D models without off-diagonal correlations, and ${W}_{c}\ensuremath{\sim}{n}^{1/2}lnn$ for QREM. The key difference between the QD and 1D models is in the structure of correlations of many-body energies. Removing off-diagonal Fock-space correlations makes both these models ``maximally chaotic''. Our findings demonstrate that the scaling of
Wc(n) for MBL transitions is governed by a combined effect of Fock-space correlations of diagonal and off-diagonal matrix elements.
We have investigated the dynamics of bound particles in multilevel current-carrying quantum dots. We look specifically in the regime of resonant tunnelling transport, where several channels are available for transport. Through a non-Markovian formalism under the Born approximation, we investigate the real-time evolution of the confined particles including transport-induced decoherence and relaxation. In the case of a coherent superposition between states with different particle number, we find that a Fock-space coherence may be preserved even in the presence of tunneling into and out of the dot. Real-time results are presented for various asymmetries of tunneling rates into different orbitals.
Many-body-localization (MBL) transitions are studied in a family of single-spin-flip spin- 1 2 models, including the one-dimensional (1D) chain with nearest-neighbor interactions, the quantum dot (QD) model with all-to-all pair interactions, and the quantum random energy model (QREM). We investigate the generalized imbalance that characterizes propagation in Fock space out of an initial basis state and, at the same time, can be efficiently probed by real-space measurements. For all models considered, the average imbalance and its quantum and mesoscopic fluctuations provide excellent indicators for the position of the MBL transition W c ( n ) , where n is the number of spins. Combining these findings with earlier results on level statistics, we determine phase diagrams of the MBL transitions in the n − W plane. Our results provide evidence for a direct transition between the ergodic and MBL phases for each of the models, without any intermediate phase. For QREM and QD model, W c ( n ) grows as a power law of n (with logarithmic corrections), in agreement with analytical predictions W c QREM ( n ) ∼ n 1 / 2 ln n and W c QD ( n ) ≳ n 3 / 4 ln 1 / 2 n . This growth is in stark contrast to the 1D model, where W c ( n ) is essentially independent of n , consistent with the analytic expectation W c 1 D ( n → ∞ ) = const . We also determine the scaling of the transition width Δ W ( n ) / W c ( n ) and estimate the system size n needed to study the asymptotic scaling behavior. Although the corresponding values of n are larger than those accessible to exact simulations on a classical computer, they are within the reach of quantum simulators. Our results indicate feasibility of experimental studies of n − W phase diagrams and scaling properties of MBL transitions in models of 1D and QD type and in their extensions to other spatial geometry or distance-dependent interactions.