Spin-charge separation in two dimensions: spinon-chargon gauge theories from duality

TL;DR

This paper develops a dual gauge theory framework to describe spin-charge separation in two-dimensional electron systems, analyzing vortex structures and proposing methods to construct Hamiltonians for exotic fractional phases.

Contribution

It introduces a dual gauge theory approach for spin-charge separation in 2D systems and demonstrates its application through coupled-wire duality and Hamiltonian construction.

Findings

Formulation of a compact gauge theory for spinons and chargons.

Exact duality implementation using coupled-wire arrays.

Method to construct parent Hamiltonians for fractional phases.

Abstract

Strong interactions between electrons in two dimensions can realize phases where their spins and charges separate. We capture this phenomenon within a dual formulation. Focusing on square lattices, we analyze the long-wavelength structure of vortices when the microscopic particles -- electrons or spinful bosons -- are near half-filling. These conditions lead to a compact gauge theory of spinons and chargons, which arise as the fundamental topological defects of the low-energy vortices. The gauge theory formulation is particularly suitable for studying numerous exotic phases and transitions. We support the general analysis by an exact implementation of the duality of a coupled-wire array. Finally, we demonstrate how the latter can be exploited to construct parent Hamiltonians for fractional phases and their transitions.