Quantum Nonlinear Sigma Model for Arbitrary Spin Heisenberg Antiferromagnets

TL;DR

This paper derives a quantum nonlinear sigma model for arbitrary spin Heisenberg antiferromagnets, providing explicit S-dependent parameters and validating results against experimental and numerical data.

Contribution

It introduces a generalized QNLSM for arbitrary S and explicitly calculates its parameters, extending previous models.

Findings

Spin wave velocity matches experimental data for La2CuO4

Correlation lengths for 2D QHA agree with numerical results

Predicted spin gaps for 1D QHA align with simulations

Abstract

In this Letter, we derive a quantum nonlinear sigma model (QNLSM) for quantum Heisenberg antiferromagnets (QHA) with arbitrary S (spin) values. A upper limit of the low temperature is naturally carried out for the reliability of the QNLSM. The S dependence of the effective coupling constant and the spin wave velocity in the QNLSM are also obtained explicitly. The resulting spin wave velocity for 2-dim spin-1/2 QHA highly concurs with the experimental data of high $T_c$ compound La2CuO4. The predicted correlation lengths for 2d QHA and spin-gap magnitudes for 1d QHA also agrees with the accurate numerical results.