Fourfold degenerate columnar-dimer ground state in square lattice antiferromagnets

TL;DR

This paper introduces two frustrated quantum spin models on a square lattice with a fourfold degenerate columnar-dimer ground state, exploring their phase transitions and ground state properties.

Contribution

The study constructs exactly solvable models with degenerate dimer ground states and analyzes their phase transitions using bond-operator mean-field theory.

Findings

Exact fourfold degenerate columnar-dimer ground state identified

Quantum phase diagram shows continuous transition to Néel or collinear phases

Ground state evolution mapped via mean-field analysis

Abstract

We construct and study two frustrated quantum spin-1/2 models on square lattice, which are like the antiferromagnetic $J_1$-$J_2$ model with some additional four-spin exchange interactions. These models admit an exactly solvable case in which the ground state consists of four degenerate columnar-dimer singlet (CDS) configurations. Away from the exact case, we employ bond-operator mean-field theory to investigate the evolution of the ground state by varying the interaction parameters. The mean-field calculation reveals a quantum phase diagram in which the CDS phase undergoes a continuous phase transition to either N\'eel or collinear ordered antiferromagnetic phases.