Localised pair formation in bosonic flat-band Hubbard models

TL;DR

This paper rigorously demonstrates localized pair formation in the ground states of bosonic flat-band Hubbard models on line graphs, using spectral bounds and eigenstate analysis, including new examples of 2D graphs.

Contribution

It introduces a generalized Gershgorin's circle theorem approach to establish energy bounds and proves localized pair formation in broad classes of line graphs, including novel 2D examples.

Findings

Rigorous energy bounds for lowest states above critical filling

Eigenstates dominated by localized pairs

Proof of localized pairs in specific 2D graphs

Abstract

Using a generalised version of Gershgorin's circle theorem, rigorous boundaries on the energies of the lowest states of a broad class of line graphs above a critical filling are derived for hardcore bosonic systems. Also a lower boundary on the energy gap towards the next lowest states is established. Additionally, it is shown that the corresponding eigenstates are dominated by a subspace spanned by states containing a compactly localised pair and a lower boundary for the overlap is derived as well. Overall, this strongly suggests localised pair formationin the ground states of the broad class of line graphs and rigorously proves it for some of the graphs in it, including the inhomogeneous chequerboard chain as well as two novel examples of regular two dimensional graphs.