Universal properties of frustrated spin systems: 1/N-expansion and renormalization group approaches

Abstract

We consider a quantum two-dimensional O(N)xO(2)/O(N-2)xO(2) nonlinear sigma model for frustrated spin systems and formulate its 1/N-expansion which involves fluctuating scalar and vector fields describing kinematic and dynamic interactions, respectively. The ground state phase diagram of this model is obtained within the 1/N-expansion and 2+εrenormalization group approaches. The temperature dependence of correlation length in the renormalized classical and quantum critical regimes is discussed. In the region of the symmetry broken ground state ρ_in<ρ_out, χ_in<χ_out (rho_in,out and chi_in,out are the in- and out-of-plane spin stiffnesses and susceptibilities), where the mass M_μof the vector field can be arbitrarily small, physical properties at finite temperatures are universal functions of rho_in,out, chi_in,out, and temperature T. For small M_μthese properties show a crossover from low- to high temperature regime at T \sim M_μ. For ρ_in>ρ_out or χ_in>χ_out finite-temperature properties are universal functions only at sufficiently large M_μ. The high-energy behaviour in the latter regime is similar to the Landau-pole dependence of the physical charge e in quantum electrodynamics, with mass M_μplaying a role of e^{-1}. The application of the results obtained to the triangular-lattice Heisenberg antiferromagnet is considered.

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• Universal Berezinskii-Kosterlitz-Thouless dynamic scaling in the intermediate timerange in frustrated Heisenberg antiferromagnets on triangular lattice
• Antiferromagnetic and spin spiral correlations in the doped two-dimensional Hubbard model: gauge symmetry, Ward identities, and dynamical mean-field theory analysis