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.
Highlights
Tight-binding models of interacting particles with a flat band, i.e., a set of highly degenerate single-particle energy eigenstates, have been studied intensively over the decades
We present some results of Monte Carlo simulation of the loop-gas model, which strongly indicates that the two-dimensional model undergoes a Kosterlitz-Thouless (KT) transition and exhibits quasi-off-diagonal long-range order (ODLRO) in its ground states
We proposed a class of exactly solvable models of interacting bosons with a flat band and argued that the Mottinsulator-like ground states may exhibitBEC
Summary
Tight-binding models of interacting particles with a flat band, i.e., a set of highly degenerate single-particle energy eigenstates, have been studied intensively over the decades. In this paper we propose a class of tight-binding systems of interacting bosons with a flat lowest band. It was found that these states do not exhibit off-diagonal (quasi) long-range order It was found in a two-component system of bosons that one component may exhibit Bose-Einstein condensation (BEC) while the other is in the Mott insulating state [16]. We stress that our ground states maintain a Mott-insulatorlike nature even when they exhibit (quasi-)ODLRO. This is most clearly seen in the anomalously small particlenumber fluctuation observed in a specific setting. It would be exciting if our exactly solvable model provides an example of a novel exotic phase of matter where a Mott-insulator-like nature and (quasi-)ODLRO coexist. We hope that this paper opens a new direction in the research of quantum many-body systems
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