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

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

1993-04-27

arxiv.org/abs/cond-mat/9304046v5

Physical Review B 49, 11919 (1994)

Physics

Condensed Matter

81 pages, REVTEX 3.0, smaller updated version, YCTP-xxxx

Scientific paper

10.1103/PhysRevB.49.11919

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 N\'{e}el order. For N\'{e}el-ordered states, `nearly-critical' means that the ground state spin-stiffness, $\rho_s$, satisfies $\rho_s \ll J$, where $J$ is the nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered ground states have a energy-gap, $\Delta$, towards excitations with spin-1, which satisfies $\Delta \ll J$. 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 $La_{2-\delta} Sr_{\delta}Cu O_4$.

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