Valence bond solid phases in a cubic antiferromagnet

TL;DR

This study uses quantum Monte Carlo simulations to explore valence bond solid phases in a cubic antiferromagnet, revealing two distinct VBS states and first-order phase transitions, thus providing insights into exotic quantum phase transitions.

Contribution

It introduces a detailed simulation of cubic lattice quantum Heisenberg models with higher-order interactions, identifying two novel valence bond solid phases and their phase boundaries.

Findings

Identified two different valence bond solid ground states.

Observed strongly first-order phase transitions between phases.

Strengthened understanding of exotic quantum phase transitions.

Abstract

We report on a valence bond projector Monte Carlo simulation of the cubic lattice quantum Heisenberg model with additional higher-order exchange interactions in each unit cell. The model supports two different valence bond solid ground states. In one of these states, the dimer pattern is a three-dimensional analogue of the columnar pattern familiar from two dimensions. In the other, the dimers are regularly arranged along the four main diagonals in 1/8 of the unit cells. The phases are separated from one other and from a Neel phase by strongly first order boundaries. Our results strengthen the case for exotic transitions in two dimensions, where no discontinuities have been detected at the Heisenberg Neel-VBS transition driven by four-spin plaquet interactions.