Abstract
We systematically study the effect of disorder and interactions on a quasi-one dimensional diamond chain possessing flat bands. Disorder localizes all the single particle eigenstates, while at low disorder strengths we obtain weak flat-band based localization (FBL), at high disorder strengths, we see conventional Anderson localization (AL). The compactly localized (CL) eigenstates of flat bands show a persisting oscillatory recurrence in the study of single-particle wavepacket dynamics. For low disorder a damped oscillatory recurrence behavior is observed which is absent for high disorder. Non-interacting many particle fermion states also follow the same trend except showing a delocalizing tendency at intermediate disorder due to the fermionic statistics in the system. As interactions are switched on, for the finite-sizes that we are able to study, a non-ergodic `mixed phase' is observed at low disorder which is separated from the MBL phase at high disorder by a thermal phase at intermediate-disorder. A study of many-body nonequilibrium dynamics reinforces these findings.
Highlights
Invariant Hermitian systems possessing flat bands (FBs) [1,2,3] exhibit remarkable properties, which emanate from the compactly localized eigenstates (CLS) associated with them
One main observation we make through this study is that, even though the inverse participation ratio (IPR) in the weak flat-band based localization (FBL) states are obtained to be independent of disorder [Fig. 3(a)], a closer examination of fidelity (Fig. 4) reveals that the nature of eigenstates changes substantially with disorder strength
Disorder detunes and hybridizes the compact localized states associated with flat bands and as the strength of disorder is increased, flat-band based localization and conventional Anderson localization are observed
Summary
Invariant Hermitian systems possessing flat bands (FBs) [1,2,3] exhibit remarkable properties, which emanate from the compactly localized eigenstates (CLS) associated with them. These states are called compact because they reside on a finite volume of the lattice and strictly vanish elsewhere [4,5,6,7,8]. We study level statistics, many-body IPR and nonequilibrium dynamics of the revival probability, entanglement entropy and imbalance parameter to obtain insights into the properties of many-particle states in the interacting system.
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