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Field Theories of Frustrated Heisenberg Antiferromagnets

Sumathi Rao·Diptiman Sen
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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).

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Sumathi Rao, Diptiman Sen. 1995-07-02. Field Theories of Frustrated Heisenberg Antiferromagnets. https://doi.org/10.1088/0953-8984%2F9%2F8%2F012

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