Competing orders in a frustrated Heisenberg model on the Fisher lattice

TL;DR

This paper explores the complex magnetic phases of a frustrated Heisenberg model on the Fisher lattice, revealing degenerate states, Dirac nodal features, and various valence bond solid orders through classical and quantum analyses.

Contribution

It provides a comprehensive analysis combining classical Monte Carlo, spin-wave, and bond operator methods to uncover novel magnetic and valence bond phases in the model.

Findings

Degenerate antiferromagnetic chain phase persists at finite temperature.

Dirac nodal loops and lines in the spin-wave spectrum.

Rich ground-state phase diagram with valence bond solid orders.

Abstract

We investigate the Heisenberg model on a decorated square (Fisher) lattice in the presence of first-neighbor $J_{1}$, second-neighbor $J_{2}$, and third-neighbor $J_{3}$ exchange couplings, with antiferromagnetic $J_{1}$. The classical ground-state phase diagram obtained within a Luttinger-Tisza framework is spanned by two antiferromagnetically ordered phases, and an infinitely degenerate antiferromagnetic chain phase. Employing classical Monte Carlo simulations we show that thermal fluctuations fail to lift the degeneracy of the antiferromagnetic chain phase. Interestingly, the spin-wave spectrum of the N\'eel state displays three Dirac nodal loops out of which two are symmetry protected while for the antiferromagnetic chain phase we find symmetry-protected Dirac lines. Furthermore, we investigate the spin $S=\frac{1}{2}$ limit employing a bond operator formalism which captures the singlet-triplet dynamics, and find a rich ground-state phase diagram host to a variety of valence bond solid orders in addition to antiferromagnetically ordered phases.