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

TL;DR

This paper develops a 1/N-expansion and renormalization group analysis of a quantum nonlinear sigma model for frustrated spin systems, revealing universal properties and phase diagrams relevant to triangular-lattice antiferromagnets.

Contribution

It introduces a novel 1/N-expansion framework for frustrated spin systems and analyzes their universal finite-temperature properties and phase behavior.

Findings

Universal finite-temperature properties depend on spin stiffnesses and susceptibilities.

Crossover from low to high temperature occurs at T ~ M_mu for small vector field mass.

High-energy behavior resembles Landau-pole dependence in QED.

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+\epsilon renormalization 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 \rho_in<\rho_out, \chi_in<\chi_out (rho_in,out and chi_in,out are the in- and out-of-plane spin stiffnesses and susceptibilities), where the mass M_\mu of 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_\mu these properties show a crossover from low- to high temperature regime at T \sim M_\mu. For \rho_in>\rho_out or \chi_in>\chi_out finite-temperature properties are universal functions only at sufficiently large M_\mu. 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_\mu playing a role of e^{-1}. The application of the results obtained to the triangular-lattice Heisenberg antiferromagnet is considered.