Separation of Spin and Charge Quantum Numbers in Strongly Correlated Systems

TL;DR

This paper investigates the conditions under which spin and charge degrees of freedom separate in two-dimensional strongly correlated systems, using a Heisenberg model with a focus on the s-RVB phase and flux states.

Contribution

It establishes sufficient conditions for spin-charge separation, introduces a local SU(2) gauge symmetry framework, and analyzes the phase transition into a flux state in a 2D Heisenberg model.

Findings

Identification of the s-RVB phase with a finite spinon gap

Existence of a second order phase transition to a flux state

Contrast between 2D deconfined spinons and confined 1D spinons

Abstract

In this paper we reexamine the problem of the separation of spin and charge degrees of freedom in two dimensional strongly correlated systems. We establish a set of sufficient conditions for the occurence of spin and charge separation. Specifically, we discuss this issue in the context of the Heisenberg model for spin-1/2 on a square lattice with nearest ($J_1$) and next-nearest ($J_2$) neighbor antiferromagnetic couplings. Our formulation makes explicit the existence of a local SU(2) gauge symmetry once the spin-1/2 operators are replaced by bound states of spinons. The mean-field theory for the spinons is solved numerically as a function of the ratio $J_2/J_1$ for the so-called s-RVB Ansatz. A second order phase transition exists into a novel flux state for $J_2/J_1>(J_2/J_1)_{{\rm cr}}$. We identify the range $0<J_2/J_1<(J_2/J_1)_{\rm cr}$ as the s-RVB phase. It is characterized by the existence of a finite gap to the elementary excitations (spinons) and the breakdown of all the continuous gauge symmetries. An effective continuum theory for the spinons and the gauge degrees of freedom is constructed just below the onset of the flux phase. We argue that this effective theory is consistent with the deconfinement of the spinons carrying the fundamental charge of the gauge group. We contrast this result with the study of the one dimensional quantum antiferromagnet within the same approach. We show that in the one dimensional model, the spinons of the gauge picture are always confined and thus cannot be identified with the gapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.