We investigate the feasibility of identifying many-body localization in semiconductor quantum dot arrays within current experimental capabilities. Using an extended Fermi-Hubbard model parameterized by realistic device conditions, we analyze the phase diagram through a set of observables with varying experimental accessibility. Our results demonstrate that signatures of MBL can, in principle, be accessed in present-day quantum dot platforms. Crucially, we show that the widely used imbalance fails to distinguish between interaction-induced freezing and genuine localization, highlighting the importance of carefully selecting and interpreting experimental probes. We identify observables that can reliably distinguish genuine MBL from interaction-induced effects, thereby establishing practical criteria for detecting localization in realistic quantum dot arrays.
Anderson localization on random regular graphs (RRG) serves as a toy-model of many-body localization (MBL). We explore the transition from ergodicity to localization on RRG with large connectivity
m. In the analytical part, we focus on the inverse participation ratio of eigenstates and identify several regimes on the ergodic side of the transition---self-consistent golden rule, golden rule, precritical, and critical---that the system consecutively goes through when the disorder increases toward the point
Wc of the localization transition. We also perform exact-diagonalization numerics as well as a population-dynamics analysis combining analytical and numerical techniques. Results of all the approaches are in excellent mutual agreement. We further explore the evolution from ergodicity to localization in two models of Fock-space MBL: fermionic and spin quantum dots. Large-connectivity RRG models serve as an approximation for this class of many-body problems; one of our central goals is to better understand the status of this approximation. Our numerical simulations support the conjecture that, in the limit of a large system, there is a sharp ergodicity-to-localization transition in the quantum-dot models. Furthermore, our results are consistent with the RRG-like scaling of the critical disorder, ${W}_{c}\ensuremath{\sim}mlnm$. While in the golden-rule range the behavior of quantum-dot models is in agreement with analytical predictions based on the RRG model, substantial deviations occur in the precritical regime. Our results indicate that the precritical and critical behavior (as well as the numerical coefficient in the formula for
Wc) in the quantum-dot models may be different from what one would expect from the RRG-like approximation.
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.