Ground States and Dynamical Properties of $S>1/2$ Quantum Heisenberg Model on the 1/5-Depleted Square Lattice

TL;DR

This study investigates the quantum phases and dynamic properties of the $S>1/2$ Heisenberg model on a 1/5-depleted square lattice, revealing phase transitions, critical points, and excitation spectra relevant for neutron scattering experiments.

Contribution

It provides the first comprehensive numerical analysis of the phase diagram and dynamical spin structure factors for the $S>1/2$ Heisenberg model on this lattice, including critical points and excitation signatures.

Findings

Identified three quantum phases: dimer, Néel, and plaquette valence bond solid.

Determined quantum critical points belonging to the O(3) universality class.

Characterized low-energy excitations as triplons, magnons, and spinon continua.

Abstract

We study the $S>1/2$ antiferromagnetic Heisenberg model on the 1/5-depleted square lattice as a function of the ratio of the intra-plaquette coupling to the inter-plaquette coupling. Using stochastic series expansion quantum Monte Carlo simulations, we numerically identify three quantum phases, including the dimer phase, N\'eel phase and plaquette valence bond solid phase. We also obtain the accurate quantum critical points that belong to the O(3) universality class using the large-scale finite-size scaling. Most importantly, we study the dynamic spin structure factors of different phases, which can be measured by inelastic neutron scattering experiments. The low-energy excitations can be explained as triplons in the dimer phase and plaquette valence bond solid phase. While in the N\'eel phase, the more prominent magnon mode can be found as the spin magnitude increases. Furthermore, we find a broader continuum at smaller $S$, which may be the dynamical signature of nearly deconfined spinon excitations.