Effective field theory for S=1 quantum nematic

TL;DR

This paper develops an effective field theory for S=1 quantum nematic systems, revealing how quantum and thermal fluctuations influence order and excitations, and introduces topological features in the low-energy description.

Contribution

It derives a low-energy RP^{2} nonlinear sigma-model for S=1 quantum nematic phases, including topological instantons and analysis of fluctuations in different dimensions.

Findings

Quantum fluctuations destroy long-range order in 1D, leading to a gapped spin liquid.

In 2D, thermal fluctuations prevent long-range nematic order at finite temperature.

Topological instantons with  charge are constructed in the model.

Abstract

For S=1 system with general isotropic nearest-neighbor exchange, we derive the low-energy description of the spin nematic phase in terms of the RP^{2} nonlinear sigma-model. In one dimension, quantum fluctuations destroy long-range nematic (quadrupolar) ordering, leading to the formation of a gapped spin liquid state being an analog of the Haldane phase for a spin nematic. Nematic analog of the Belavin-Polyakov instanton with \pi_{2} topological charge 1/2 is constructed. In two dimensions the long-range order is destroyed by thermal fluctuations and at finite temperature the system is in a renormalized classical regime. Behavior in external magnetic field is discussed.