Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4

TL;DR

This paper develops a theory for how quenched disorder affects valence-bond solids and quantum spin liquids in 2D, with applications to YbMgGaO4, predicting experimental signatures consistent with observed phenomena.

Contribution

It introduces a theoretical framework for disordered quantum magnets, connecting valence-bond physics with topological defects and applying it to YbMgGaO4.

Findings

Weak disorder destroys valence-bond solid phases, creating spin-1/2 defects.

Disorder leads to a strongly random spin network with low-energy excitations.

Predicted experimental signatures match observations in YbMgGaO4.

Abstract

We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2d valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1/2 magnetic moments, and whose residual interactions decide the ultimate low energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin-1/2 per statistical unit cell. These conjectures are supported by an argument for 1d spin chains. We apply insights from this study to the phenomenology of YbMgGaO$_4$, a recently discovered triangular lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO$_4$ and related materials.