Emergence of a Dimer-Dimer Interaction in the Low-Energy Effective Quantum-Dimer Model of a Diamond-Like-Decorated Square-Lattice Heisenberg Antiferromagnets with Further Neighbor Couplings

TL;DR

This paper investigates how additional further neighbor couplings in a diamond-like-decorated square-lattice Heisenberg antiferromagnet induce a dimer-dimer interaction in the effective quantum-dimer model, potentially stabilizing specific dimer phases.

Contribution

It introduces a new type of further neighbor coupling that results in an attractive dimer-dimer interaction, extending previous models which had no such interaction.

Findings

Introduction of a second neighbor coupling induces dimer-dimer attraction.

The v/t ratio varies with the exchange parameter ratio.

Results suggest stabilization of the columnar phase.

Abstract

We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice perturbed by two kinds of further neighbor couplings. In our previous study [J. Phys. Soc. Jpn. 85, 094002 (2016)], the second-order effective Hamiltonian for the Heisenberg model perturbed by a further neighbor coupling was found to be a square-lattice quantum-dimer model with a finite hopping amplitude, t>0, and no dimer-dimer interaction, v=0. In this study, we introduce another kind of further neighbor coupling and show that it leads to an attractive interaction between dimers, which suggests the stabilization of the columnar phase of the square-lattice quantum-dimer model. The calculated v/t is presented as a function of the ratio of the two exchange parameters in the Heisenberg model.