Theory of two-dimensional antiferromagnets with a nearly critical ground state (abstract)

Abstract

We present the general theory of clean, two-dimensional, quantum Heisenberg antiferromagnets which are close to the zero-temperature quantum transition between ground states with and without long-range Néel order. For Néel-ordered states, ‘‘nearly-critical’’ means that the ground state spin stiffness, ρs, satisfies ρs≪J, where J is the nearest-neighbor exchange constant, while ‘‘nearly-critical’’ quantum-disordered ground states have an energy gap, Δ, towards excitations with spin-1, which satisfies Δ≪J. The allowed temperatures, T, are also smaller than J, but no restrictions are placed on the values of kBT/ρs or kBT/Δ. Under these circumstances, we show that the wave vector /frequency-dependent uniform and staggered spin susceptibilities, and the specific heat, are completely universal functions of just three thermodynamic parameters. On the ordered side, these three parameters are ρs, the T=0 spin-wave velocity c, and the ground state staggered moment N0. Explicit results for the universal scaling functions are obtained by a 1/N expansion on the O(N) quantum nonlinear sigma model. These calculations lead to a variety of testable predictions for neutron scattering, NMR, and magnetization measurements. Our results are in good agreement with a number of numerical simulations and experiments on undoped and lightly doped La2−δSrδCuO4.