Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions

TL;DR

This paper unifies parton gauge theories and coupled-wire models to better understand quantum magnetism in two dimensions, enabling new calculations of correlations and Hamiltonians for exotic spin liquid phases.

Contribution

It introduces a unified framework linking parton gauge theories with coupled-wire constructions for 2D quantum spin systems, facilitating analysis of complex phases.

Findings

Derived explicit relations between spin operators and emergent quasiparticles.

Developed an algorithm for constructing parent Hamiltonians for exotic phases.

Applied the approach to several chiral and non-chiral quantum spin liquids.

Abstract

The fractionalization of microscopic degrees of freedom is a remarkable manifestation of strong interactions in quantum many-body systems. Analytical studies of this phenomenon are primarily based on two distinct frameworks: field theories of partons and emergent gauge fields, or coupled arrays of one-dimensional quantum wires. We unify these approaches for two-dimensional spin systems. Via exact manipulations, we demonstrate how parton gauge theories arise in microscopic wire arrays and explicitly relate spin operators to emergent quasiparticles and gauge-field monopoles. This correspondence allows us to compute physical correlation functions within both formulations and leads to a straightforward algorithm for constructing parent Hamiltonians for a wide range of exotic phases. We exemplify this technique for several chiral and non-chiral quantum spin liquids.