Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system

TL;DR

This paper constructs a quantum dimer model on a square lattice exhibiting a line of critical points and a Kosterlitz-Thouless transition, with implications for understanding quantum phase transitions in two-dimensional systems.

Contribution

It introduces a local interacting quantum dimer model with a critical line and analyzes its phase diagram, including the transition inherited from a classical Kosterlitz-Thouless transition.

Findings

Identifies a line of critical points separating valence bond crystal phases.

Shows the critical line terminates at a quantum Kosterlitz-Thouless transition.

Proposes a generalized dilute dimer model with monomers.

Abstract

We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interactions that can be used to suppress the line of critical points by gradually shrinking it to a single point. Finally, we propose a way to generalize the quantum Hamiltonian to a dilute dimer model in presence of monomers and we qualitatively discuss the phase diagram.