Method to characterize spinons as emergent elementary particles

TL;DR

This paper introduces a quantum Monte Carlo-based method to characterize spinons as emergent particles in various quantum spin models across dimensions, revealing their particle-like nature in different quantum states.

Contribution

The paper presents a novel technique to directly study and define spinons in quantum spin models using wave-function overlaps and correlation functions, applicable in any dimension.

Findings

Spinons are well-defined in valence-bond-solid states.

Spinons are marginally defined in Heisenberg critical states.

Spinons are not well-defined in Néel ordered states.

Abstract

We develop a technique to directly study spinons (emergent spin S = 1/2 particles) in quantum spin models in any number of dimensions. The size of a spinon wave packet and of a bound pair (a triplon) are defined in terms of wave-function overlaps that can be evaluated by quantum Monte Carlo simulations. We show that the same information is contained in the spin-spin correlation function as well. We illustrate the method in one dimension. We confirm that spinons are well defined particles (have exponentially localized wave packet) in a valence-bond-solid state, are marginally defined (with power-law shaped wave packet) in the standard Heisenberg critical state, and are not well defined in an ordered N\'eel state (achieved in one dimension using long-range interactions).