The Rokhsar-Kivelson Model of Quantum Dimers as a Gas of Free Fermionic Strings

TL;DR

This paper demonstrates that the 2+1D quantum dimer model on a square lattice can be mapped to a system of free fermionic strings, revealing insights into its phase and excitation spectrum.

Contribution

It introduces a Jordan-Wigner construction for string operators and establishes the equivalence of the dimer model to free fermionic strings, providing bounds on energy and tension.

Findings

System is in a spin-fluid phase

No gap in the excitation spectrum

Topological defects are linearly confined

Abstract

The $2+1$-dimensional quantum dimer model on a square lattice, proposed by Rokhsar and Kivelson as a theory of layered superconductivity, is shown to be equivalent to a many-body theory of free, transversely oscillating strings obeying Fermi statistics. A Jordan-Wigner construction for string field operators is presented. Topological defects are shown to be linearly confined in pairs by dynamical strings. Exact upper and lower bounds are placed on the ground-state energy and the string tension. It is argued that the system is in a spin-fluid phase and that there is no gap in the excitation spectrum.