Many-body localization transition from flat-band fine tuning

Carlo Danieli,Alexei Andreanov,Sergej Flach

doi:10.1103/physrevb.105.l041113

Abstract

Translationally invariant flatband Hamiltonians with interactions lead to a many-body localization transition. Our models are obtained from single-particle lattices hosting a mix of flat and dispersive bands, and equipped with fine-tuned two--body interactions. Fine-tuning of the interaction results in an extensive set of local conserved charges and a fragmentation of the Hilbert space into irreducible sectors. In each sector, the conserved charges originate from the flatband and act as an effective disorder inducing a transition between ergodic and localized phases upon variation of the interaction strength. Such fine-tuning is possible in arbitrary lattice dimensions and for any many-body statistics. We present computational evidence for this transition with spinless fermions.

Highlights

The celebrated Anderson localization [1] with additional interactions leads to a novel phase of matter dubbed many-body localization (MBL)
Flatband lattices and compact localized (eigen)states (CLS) have been extensively studied over the last decades [26,27,28], and the vast majority of results concern single-particle problems, e.g., lattice generator schemes [29,30,31,32,33,34,35,36]—flatbands are progressively entering the realm of quantum many-body physics
We show that disorder free MBL needs just one flatband and at least one dispersive band when accompanied with a proper interaction fine-tuning

Summary

Introduction

The celebrated Anderson localization [1] with additional interactions leads to a novel phase of matter dubbed many-body localization (MBL). We show that disorder free MBL needs just one flatband and at least one dispersive band when accompanied with a proper interaction fine-tuning. Our results explain recent reports on MBL-like dynamics for interacting spinless fermions in particular flatband lattices [47].

Results

Conclusion