SO(3) nonlinear $\sigma$ model for a doped quantum helimagnet

Abstract

A field theory describing the low-energy, long-wavelength sector of an incommensurate, spiral magnetic phase is derived from a spin-fermion model that is commonly used as a microscopic model for high-temperature superconductors. After integrating out the fermions in a path-integral representation, a gradient expansion of the fermionic determinant is performed. This leads to an O(3)$\otimes$O(2)-symmetric quantum nonlinear $\sigma$ model, where the doping dependence is explicitly given by generalized fermionic susceptibilities which enter into the coupling constants of the $\sigma$ model and contain the fermionic band-structure that results from the spiral background. A stability condition of the field theory self-consistently determines the spiral wavevector as a function of the doping concentration. Furthermore, terms of topological nature like the $\theta$-vacuum term in (1+1)-dimensional nonlinear $\sigma$ models are obtained for the plane of the spiral.

43 pages, RevTex, amsfonts, no figures, available at ftp://ftp.physik.uni-wuerzburg.de/pub/preprint/1996/WUE-ITP-96-004.ps.gz, to be published in Nuclear Physics B

References in corpus (7)

• Finite size and temperature effects in the AF Heisenberg model
• Universal Magnetic Properties of Frustrated Quantum Antiferromagnets in Two Dimensions
• Quantum Phase Transition in Frustrated Two-Dimensional Antiferromagnets
• A Renormalization Group Study of Helimagnets in D=2+EPSILON Dimensions
• Quantum Phases of the Shraiman-Siggia Model
• The massive $C{P}^{N-1}$ model for frustrated spin systems
• Semi-classical description of the frustrated antiferromagnetic chain

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• SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model
• Fermi Surface and Spectral Functions of a Hole Doped Spin-Fermion Model for Cuprates
• Effect of Non-Magnetic Impurities (Zn,Li) in a Hole Doped Spin-Fermion Model for Cuprates
• Topological Defects and the Spin Glass Phase of Cuprates
• Massive CP${}^1$ theory from a microscopic model for doped antiferromagnets
• Effect of Adiabatic Phonons on Striped and Homogeneous Ground States
• Dissipative dynamics of topological defects in frustrated Heisenberg spin systems