Quantum nonlinear σ model for arbitrary spin heisenberg antiferromagnets

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 2D spin-1/2 QHA highly concurs with the experimental data of high Tc compound La2CuO4. The predicted correlation lengths for 2D QHA and spin-gap magnitudes for 1D QHA also agrees with the accurate numerical results.