Spinons in more than one dimension: Resonance Valence Bond state stabilized by frustration

TL;DR

This paper proves the existence of spinons, neutral spin-1/2 excitations, in frustrated magnetic models across multiple dimensions using non-perturbative methods and bosonization techniques.

Contribution

It provides a non-perturbative proof of spinon existence in anisotropic frustrated magnets, including models with static and dynamic frustration, using an alternative bosonization approach.

Findings

Existence of propagating spin-1/2 excitations (spinons) in the models.

Derivation of a low-energy effective action without constraints.

Analysis of exactly solvable limits and general case discussion.

Abstract

For two spatially anisotropic, SU(2)-invariant models of frustrated magnets in arbitrary space dimension we present a non-perturbative proof of the existence of neutral spin-1/2 excitations (spinons). In one model the frustration is static and based on fine tuning of the coupling constants, whereas in the other it is dynamic and does not require adjusting of the model parameters. For both models we derive a low-energy effective action which does not contain any constraints. Though our models admit the standard gauge theory treatment, we follow an alternative approach based on Abelian and non-Abelian bosonization. We prove the existence of propagating spin-1/2 excitations (spinons) and consider in detail certain exactly solvable limits. A qualitative discussion of the most general case is also presented.