Invariant spin coherent states and the theory of quantum antiferromagnet in a paramagnetic phase

TL;DR

This paper develops a rotation-invariant path integral theory for quantum antiferromagnets in the disordered phase, combining spin wave and nonlinear sigma model approaches to analyze spin fluctuations.

Contribution

It introduces a rotation-invariant Lagrangian for the Heisenberg antiferromagnet and constructs a natural perturbation theory incorporating short and long wave fluctuations.

Findings

Derived the response function for spin fluctuations across all frequencies and wave vectors.

Calculated the free energy of the quantum antiferromagnet in the disordered phase.

Established the importance of discrete time path integral for short wave fluctuations.

Abstract

The consistent theory of the Heisenberg quantum antiferromagnet in the disordered phase with short range antiferromagnetic order was developed on the basis of the path integral for the spin coherent states. We have presented the Lagrangian of the theory in a form which is explicitly invariant under rotations and have found natural variables in the term of which one can construct a natural perturbation theory. The short wave spin fluctuations are similar to the spin wave theory ones, and the long wave spin fluctuations are governed by the nonlinear sigma model. We have also demonstrated that the short wave spin fluctuations have to be considered accurately in the framework of the discrete version in time of the path integral. In the framework of our approach we have obtained the response function for the spin fluctuations for the whole region of the frequency $\omega$ and the wave vector ${\bf k}$ and have calculated the free energy of the system.