Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice

TL;DR

This paper investigates a frustrated spin-1/2 Heisenberg model on the star lattice, revealing a novel spin-1 trimerized valence bond crystal phase induced by ferromagnetic couplings and analyzing its thermodynamic properties.

Contribution

It uncovers a fully gapped TVBC phase with emergent spin-1 degrees of freedom driven by ferromagnetic couplings in a frustrated lattice, a novel finding in this context.

Findings

Discovery of a spin-1 trimerized valence bond crystal phase.

Exponential scaling of order parameter and excitation gap with inter-triangle coupling.

Temperature dependence of specific heat matching potential experimental data.

Abstract

We explore the frustrated spin-$1/2$ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) inter-triangle couplings ($J_e<0$), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening $J_e$, the system scales exponentially, either with or without a magnetic field $h$: the order parameter, the five critical fields that separate the $J_e$-$h$ ground-state phase diagram into six phases, and the excitation gap obtained by low-temperature specific heat, all depend exponentially on $J_e$. We calculate the temperature dependence of the specific heat, which can be directly compared with future experiments.