Many-body localization due to correlated disorder in Fock space

Abstract

In presence of strong enough disorder one dimensional systems of interacting spinless fermions at non-zero filling factor are known to be in a many body localized phase. When represented in 'Fock space', the Hamiltonian of such a system looks like that of a single 'particle' hopping on a Fock lattice in the presence of a random disordered potential. The coordination number of the Fock lattice increases linearly with the system size L in one dimension. Thus in the thermodynamic limit L → ∞, the disordered interacting problem in one dimension maps on to an Anderson model with infinite coordination number. Despite this, this system displays localization which appears counterintuitive. A close observation of the on-site disorder potentials on the Fock lattice reveals a large degree of correlation among them as they are derived from an exponentially smaller number of on-site disorder potentials in real space. This indicates that the correlations between the on-site disorder potentials on a Fock lattice has a strong effect on the localization properties of the corresponding many-body system. This intuition is also consistent with studies of quantum random energy model where the typical mid-spectrum states are ergodic and the on-site potentials in Fock space are completely uncorrelated. In this work we perform a systematic quantitative exploration of the nature of correlations of the Fock space potential required for localization. We study different functional variations of the disorder correlation in Fock lattice by analyzing the eigenspectrum obtained through exact diagonalization. Without changing the typical strength of the on-site disorder potential in Fock lattice we show that changing the correlation strength can induce thermalization or localization in systems. From among the various forms of correlations we study, we find that only the linear variation of correlations with Hamming distance in Fock space is able to drive a thermal-MBL phase transition where the transition is driven by the correlation strength. Systems with the other forms of correlations we study are found to be ergodic.

Fock-space correlations and the origins of many-body localization

“…We also add here that there is a tension between our predictions and the numerical results of Ref. [42], where it was reported that a many-body localised phase can exist only if the reduced covariance ρ r has a linear variation in r/N . However, the disordered transverse-field Ising model considered in this section provides a case in contrast to this claim; for the model is well known (on analytical grounds [22]) to host a many-body localised phase, yet has a covariance (Eq.…”

Multifractality and its role in anomalous transport in the disordered XXZ spin-chain

“…Since the structure of this graph is rather involved it is normally approximated by either the Bethe lattice [33] or random-regular graphs (RRG, see also review by Imbrie et al [34]). In addition, the disorder residing on the nodes of this graph, is highly correlated, a feature which was shown to be important for MBL [35,36] compared to the Anderson problem on RRG. The first proposal of an intermediate nonergodic extended phase sandwiched between the deeply ergodic and insulating (MBL) phases appeared almost 20 years ago [33].…”

Fock-space anatomy of eigenstates across the many-body localization transition

“…The second direction, arguably more microscopically motivated, has been to study the MBL problem as an unconventional Anderson localization problem [23] on the complex, correlated Fock-space graph of a quantum many-body system [5,18,19,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. While MBL on Fock space is inherently different from conventional Anderson localization on highdimensional graphs, the latter has served as an important inspiration for the former, with regard to both techniques and the scaling laws governing the transition [43][44][45][46][47][48][49][50][51][52].…”