Field Theories of Frustrated Heisenberg Antiferromagnets

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).

Latex, 12 pages, 2 figures (gzipped and uuencoded)

References in corpus (12)

• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Resonating Valence Bond Theory of Coupled Heisenberg Chains
• Suppression of tunneling by interference in half-integer--spin particles
• Destructive quantum interference in spin tunneling problems
• DMRG Studies of the Spin-Half Heisenberg System with Dimerization and Frustration
• Numerical Study of the $S=1$ Antiferrromagnetic Spin Chain with Bond Alternation
• Semiclassical description of spin ladders
• Phase Diagram of the Spin-One Heisenberg System with Dimerization and Frustration
• Semi-classical description of the frustrated antiferromagnetic chain
• A comparative study of the phase diagrams of spin-$\frac{1}{2}$ and spin-$1$ antiferromagnetic chains with dimerization and frustration
• Non-linear Field Theory of a Frustrated Heisenberg Spin Chain
• Bosonic Mean Field Theory of the Spiral Phases of Heisenberg Antiferromagnets on a Chain

Cited by in corpus (4)

• Ordering in Cs2CuCl4: Is there a proximate spin liquid?
• Quantum phase transitions in three-leg spin tubes
• Particle Content of the Nonlinear Sigma Model with Theta-Term: a Lattice Model Investigation
• Breakdown of the Luttinger sum-rule at the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model