Massive CP$^1$ theory from a microscopic model for doped antiferromagnets

TL;DR

This paper derives a CP$^1$ field theory with a massive gauge field from a microscopic t-J model, revealing how doping can lead to incommensurate magnetic structures and deconfined spinons in antiferromagnets.

Contribution

It introduces a novel derivation of a CP$^1$ field theory with a massive gauge field from the t-J model, highlighting the emergence of incommensurate magnetic order and deconfined spinons upon doping.

Findings

Derivation of a CP$^1$ field theory with a massive gauge field from the t-J model.

Identification of incommensurate coplanar magnetic structures due to doping.

Potential for deconfined spinons in doped colinear antiferromagnets.

Abstract

A path-integral for the t-J model in two dimensions is constructed based on Dirac quantization, with an action found originally by Wiegmann (Phys. Rev. Lett. {\bf 60}, 821 (1988); Nucl. Phys. B323, 311 (1989)). Concentrating on the low doping limit, we assume short range antiferromagnetic order of the spin degrees of freedom. Going over to a local spin quantization axis of the dopant fermions, that follows the spin degree of freedom, staggered CP$^1$ fields result and the constraint against double occupancy can be resolved. The staggered CP$^1$ fields are split into slow and fast modes, such that after a gradient expansion, and after integrating out the fast modes and the dopant fermions, a CP$^1$ field-theory with a massive gauge field is obtained that describes generically incommensurate coplanar magnetic structures, as discussed previously in the context of frustrated quantum antiferromagnets. Hence, the possibility of deconfined spinons is opened by doping a colinear antiferromagnet.