Abstract
We consider some aspects of a standard model employed in studies of many-body localization: interacting spinless fermions with quenched disorder, for non-zero filling fraction, here on d-dimensional hypercubic lattices. The model may be recast as an equivalent tight-binding model on a ‘Fock-space (FS) lattice’ with an extensive local connectivity. In the thermodynamic limit exact results are obtained for the distributions of local FS coordination numbers, FS site-energies, and the density of many-body states. All such distributions are well captured by exact diagonalisation on the modest system sizes amenable to numerics. Care is however required in choosing the appropriate variance for the eigenvalue distribution, which has implications for reliable identification of mobility edges.
Highlights
In recent years there has been great interest in the study of highly excited quantum states of disordered, interacting systems, and notably the phenomenon of manybody localization[1] (MBL); for topical reviews see e.g. [2,3]
We have considered a canonical model employed in studies of MBL: a disordered system of interacting spinless fermions, here on a d-dimensional lattice with N ≡ Ld sites and Ne fermions, for non-vanishing filling ν = Ne/N
The model can be cast as an equivalent tightbinding model on a locally connected Fock-space lattice of dimension NH ∝ ecN, the sites of which correspond to the many-particle states of the system in the absence of hopping
Summary
In recent years there has been great interest in the study of highly excited quantum states of disordered, interacting systems, and notably the phenomenon of manybody localization[1] (MBL); for topical reviews see e.g. [2,3]. One of the central models[7] extensively studied in MBL is that of interacting spinless fermions with quenched disorder, for non-zero fermion filling fractions. We consider it here, on d-dimensional hypercubic lattices. To that end we consider the distributions, over both Fock-space sites and (where relevant) disorder realisations, of the local Fock-space coordination numbers, site-energies, and many-body eigenvalues (or density of states). None of these quantities contain information about localization itself, but all reflect ‘basic’ properties of the system in an obvious sense, and understanding them is a precursor to considering localization (to which we turn in a subsequent work[8]).
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