Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation

TL;DR

This paper investigates the ground states of a frustrated checkerboard antiferromagnet, identifying a crossed-dimer valence bond solid as the ground state near a specific parameter regime, and uses a bosonic interpretation to understand low-energy physics.

Contribution

It reveals the nearly degenerate ground states of the checkerboard antiferromagnet and introduces a bosonic perspective to interpret the low-energy physics of the system.

Findings

Identification of the crossed-dimer VBS as the ground state near J1 ≈ J2

Verification of VBS stability against nematic perturbations

Prediction and numerical confirmation of weaker VBS states in the easy-plane limit

Abstract

The spin-$1/2$ model system with antiferromagnetic (AF) couplings on a $J_1$-$J_2$ checkerboard lattice, known as the planar pyrochlore model, is strongly frustrated and associated with a two-to-one dimensional crossover. Using the Projected Entangled Simplex States tensor network ansatz, we identify a large number of nearly degenerate states in the frustrated region ($J_1<J_2$). Specifically, we find the long-sought crossed-dimer valence bond solid (VBS) state to be the ground state at $J_1\lesssim J_2$, while various 1D AF correlated states take over the rest. We verify the stability of the VBS state against nematic perturbation. The corresponding bosonic picture provides an intuitive understanding of the low-energy physics. Particularly, it predicts weaker VBS states in the easy-plane limit, which we confirm numerically. Our results clarify the most essential ground state properties of this interesting system and demonstrate the usefulness of bosonic picture in dealing with frustrated magnetism.