Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions

TL;DR

This study explores the quantum and classical phases of the pyrochlore Heisenberg model with competing interactions, revealing a robust quantum spin liquid phase and the effects of various parameters on magnetic orderings.

Contribution

It introduces a comprehensive analysis of the quantum Heisenberg model on the pyrochlore lattice with $J_1$ and $J_2$ interactions using the pseudofermion functional renormalization group method, highlighting the stability of the spin liquid phase.

Findings

Quantum spin-liquid phase is stable around $J_2=0$ for $S=1/2$ and $S=1$.

Quantum fluctuations modify phase boundaries and ordering wave vectors.

No new magnetic orders are stabilized by quantum fluctuations.

Abstract

We investigate the quantum Heisenberg model on the pyrochlore lattice for a generic spin $S$ in the presence of nearest-neighbor $J_{1}$ and second-nearest-neighbor $J_{2}$ exchange interactions. By employing the pseudofermion functional renormalization group method, we find, for $S=1/2$ and $S=1$, an extended quantum-spin-liquid phase centered around $J_{2}=0$, which is shown to be robust against the introduction of breathing anisotropy. The effects of temperature, quantum fluctuations, breathing anisotropies, and a $J_{2}$ coupling on the nature of the scattering profile, and the pinch points, in particular, are studied. For the magnetic phases of the $J_{1}$-$J_{2}$ model, quantum fluctuations are shown to renormalize phase boundaries compared to the classical model and to modify the ordering wave vectors of spiral magnetic states, while no new magnetic orders are stabilized.