Abstract
We consider translationally invariant tight-binding all-bands-flat networks which lack dispersion. In a recent work [arXiv:2004.11871] we derived the subset of these networks which preserves nonlinear caging, i.e. keeps compact excitations compact in the presence of Kerr-like local nonlinearities. Here we replace nonlinear terms by Bose-Hubbard interactions and study quantum caging. We prove the existence of degenerate energy renormalized compact states for two and three particles, and use an inductive conjecture to generalize to any finite number M of participating particles in one dimension. Our results explain and generalize previous observations for two particles on a diamond chain [Vidal et.al. Phys. Rev. Lett. 85, 3906 (2000)]. We further prove that quantum caging conditions guarantee the existence of extensive sets of conserved quantities in any lattice dimension, as first revealed in [Tovmasyan et al Phys. Rev. B 98, 134513 (2018)] for a set of specific networks. Consequently transport is realized through moving pairs of interacting particles which break the single particle caging.
Highlights
The study of localization phenomena in systems of interacting particles gave rise to some of the most remarkable research streams in condensed-matter physics during the past decades
We showed that the quantum versions of classical nonlinear models exhibiting caging discussed in Ref. [28] are the only systems to feature an extended set of conserved quantities—number parity operators, first introduced in Ref. [34] for specific all bands flat (ABF) geometries
We demonstrated that the picture is more subtle: we explicitly showed the existence of macroscopically degenerate interaction-renormalized compact states for any finite number M of particles on an infinite ABF lattice N → ∞— generalizing their first observation for two spinful fermions in the AB diamond chain [36]
Summary
The study of localization phenomena in systems of interacting particles gave rise to some of the most remarkable research streams in condensed-matter physics during the past decades These phenomena arise in the absence of translation invariance, as both the first prediction of singleparticle localization [1,2] and the finite-temperature transition to many-body localized phases of weakly interacting quantum particles [3,4] have been obtained in tight-binding networks in the presence of uncorrelated spatial disorder. We prove that in the quantum case, the fine-tuning conditions for nonlinear caging imply the existence of an extensive set of conserved local number parity operators—quantities first revealed in Ref. Our results apply to lattices of any spatial dimension, explaining and generalizing previous observations for two particles in the diamond chain [36]
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