Mott Insulator-like Bose-Einstein Condensation in a Tight-Binding System of Interacting Bosons with a Flat Band

TL;DR

This paper introduces a new exactly solvable model of interacting bosons with a flat band, showing potential for Mott insulator-like states and Bose-Einstein condensation phenomena, supported by Monte Carlo simulations.

Contribution

It presents a novel class of flat-band tight-binding systems with exact ground states and links to classical loop-gas models, suggesting BEC-like behavior in low dimensions.

Findings

Exact ground state expressed via local operators

Ground state exhibits Mott insulator-like properties

Supports quasi BEC in two dimensions through simulations

Abstract

We propose a new class of tight-binding systems of interacting bosons with a flat band, which are exactly solvable in the sense that one can explicitly write down the unique ground state. The ground state is expressed in terms of local creation operators, and apparently resembles that of a Mott insulator. Based on an exact representation in terms of a classical loop-gas model, we conjecture that the ground state may exhibit quasi Bose-Einstein condensation (BEC) or genuine BEC in dimensions two and three or higher, respectively, still keeping Mott insulator-like character. Our Monte Carlo simulation of the loop-gas model strongly supports this conjecture, i.e., the ground state undergoes a Kosterlitz-Thouless transition and exhibits quasi BEC in two dimensions.