Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice

TL;DR

This study uses advanced numerical methods to investigate the ground state of the Heisenberg model on the pyrochlore lattice, providing evidence against the existence of a spin-liquid phase and revealing symmetry-breaking in the system.

Contribution

The paper introduces a combined use of RVB-like Monte Carlo and neural network quantum states to analyze the 3D pyrochlore Heisenberg model, challenging the spin-liquid hypothesis.

Findings

Identification of a phase transition between spin-liquid and ordered phases

Evidence of spontaneous inversion and rotational symmetry breaking

Questioning the existence of a featureless quantum spin-liquid

Abstract

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a RVB-like many-variable Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to $4\times 4^3$ and $4 \times 3^3$ spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin-liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.