Field Theories of Frustrated Heisenberg Antiferromagnets

TL;DR

This paper develops field theories for frustrated Heisenberg antiferromagnets, analyzing their phases and low-energy excitations, revealing a massive spin-1/2 doublet and soliton-induced degeneracies.

Contribution

It introduces a non-linear sigma model framework for different phases of frustrated antiferromagnets, including detailed analysis of the spiral phase using renormalization group methods.

Findings

Identification of a massive spin-1/2 doublet in the excitation spectrum.

Existence of $Z_2$ solitons causing degeneracy in half-integer spin systems.

Field theory unifies descriptions of Neel, spiral, and colinear phases.

Abstract

We study the Heisenberg antiferromagnetic chain with both dimerization and frustration. The classical ground state has three phases: a Neel phase, a spiral phase and a colinear phase. In each phase, we discuss a non-linear sigma model field theory governing the low energy excitations. We study the theory in the spiral phase in detail using the renormalization group. The field theory, based on an $SO(3)$ matrix-valued field, becomes $SO(3) \times SO(3)$ and Lorentz invariant at long distances where the elementary excitation is analytically known to be a massive spin-$1/2$ doublet. The field theory supports $Z_2 ~$ solitons which lead to a double degeneracy in the spectrum for half-integer spins (when there is no dimerization).