Quantum disorder versus order-out-of-disorder in the Kugel-Khomskii model

TL;DR

This paper examines the Kugel-Khomskii model to understand how quantum fluctuations influence the stability of classical states, challenging previous theories that suggested quantum effects could stabilize certain classical configurations.

Contribution

The study compares different theoretical approaches to quantum fluctuations in the Kugel-Khomskii model, revealing limitations of the classical state stabilization hypothesis.

Findings

Quantum fluctuations are stronger than previously estimated by the classical stabilization approach.

Standard RPA shows that classical states are unlikely to be stabilized by quantum effects.

The results cast doubt on the existence of quantum-disorder-induced classical states in the model.

Abstract

The Kugel-Khomskii model, the simplest model for orbital degenerate magnetic insulators, exhibits a zero temperature degeneracy in the classical limit which could cause genuine quantum disorder. Khaliullin and Oudovenko [Phys. Rev. B 56, R14 243 (1997)] suggested recently that instead a particular classical state could be stabilized by quantum fluctuations. Here we compare their approach with standard random phase approximation and show that it strongly underestimates the strength of the quantum fluctuations, shedding doubts on the survival of any classical state.