Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State

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, $ρ_s$, satisfies $ρ_s \ll J$, where $J$ is the nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered ground states have a energy-gap, $Δ$, towards excitations with spin-1, which satisfies $Δ\ll J$. Under these circumstances, we show that the wavevector/frequency-dependent uniform and staggered spin susceptibilities, and the specific heat, are completely universal functions of just three thermodynamic parameters. Explicit results for the universal scaling functions are obtained by a $1/N$ expansion on the $O(N)$ quantum non-linear sigma model, and by Monte Carlo simulations. 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 $La_{2-δ} Sr_δCu O_4$.