A Generalized Quantum Dimer Model Applied to the Frustrated Heisenberg Model on the Square Lattice: Emergence of a Mixed Columnar-Plaquette Phase

TL;DR

This paper extends the Quantum Dimer Model to higher orders for frustrated square lattice Heisenberg magnets, revealing a plaquette phase as the ground state through advanced numerical analysis.

Contribution

It introduces a generalized Quantum Dimer Model derived from an extended RK loop-expansion, applicable to frustrated magnets, and identifies a plaquette phase as the ground state.

Findings

Identification of a plaquette phase as the ground state.

Leading correction involves dimer moves on length-6 loops.

Model free of the original sign problem.

Abstract

Aiming to describe frustrated quantum magnets with non-magnetic singlet ground states, we have extended the Rokhsar-Kivelson (RK) loop-expansion to derive a generalized Quantum Dimer Model containing only connected terms up to arbitrary order. For the square lattice frustrated Heisenberg antiferromagnet (J1-J2-J3 model), an expansion up to 8th order shows that the leading correction to the original RK model comes from dimer moves on length-6 loops. This model free of the original sign problem is treated by advanced numerical techniques. The results suggest that a rotationally anisotropic plaquette phase is the ground state of the Heisenberg model in the parameter region of maximum frustration.