Confinement and Deconfinement of Spinons in Two Dimensions

TL;DR

This study uses Monte Carlo simulations to investigate spinon confinement in 2D quantum spin systems, revealing deconfinement in spin-liquid states and confinement in valence-bond solids, with critical behavior near phase transitions.

Contribution

First detailed numerical analysis of spinon confinement and deconfinement in two-dimensional quantum spin systems using Monte Carlo methods.

Findings

Spinons are deconfined in the spin-liquid state with finite size and infinite confinement length.

In valence-bond solids, spinons are confined with finite size and confinement length.

Approaching the critical point, both spinon size and confinement length diverge.

Abstract

We use Monte Carlo methods to study spinons in two-dimensional quantum spin systems, characterizing their intrinsic size $\lambda$ and confinement length $\Lambda$. We confirm that spinons are deconfined, $\Lambda \to \infty$ and $\lambda$ finite, in a resonating valence-bond spin-liquid state. In a valence-bond solid, we find finite $\lambda$ and $\Lambda$, with $\lambda$ of a single spinon significantly larger than the bound-state---the spinon is soft and shrinks as the bound state is formed. Both $\lambda$ and $\Lambda$ diverge upon approaching the critical point separating valence-bond solid and N\'eel ground states. We conclude that the spinon deconfinement is marginal in the lowest-energy state in the spin-1 sector, due to weak attractive spinon interactions. Deconfinement in the vicinity of the critical point should occur at higher energies.