Order by disorder in a four flavor Mott-insulator on the fcc lattice

TL;DR

This paper investigates the classical and quantum behaviors of the SU(4) Heisenberg model on an fcc lattice, revealing how quantum fluctuations select specific ordered states and influence finite-temperature transitions.

Contribution

It explicitly constructs all classical ground states and analyzes quantum fluctuation effects using linear flavor-wave theory on the SU(4) model.

Findings

Quantum fluctuations select a four-sublattice ordered state at zero temperature.

Flavor waves interact along specific planes, effectively reducing dimensionality.

Long-range interactions may induce finite-temperature ordering.

Abstract

The classical ground states of the SU(4) Heisenberg model on the face centered cubic lattice constitute a highly degenerate manifold. We explicitly construct all the classical ground states of the model. To describe quantum fluctuations above these classical states, we apply linear flavor-wave theory. At zero temperature, the bosonic flavor waves select the simplest of these SU(4) symmetry breaking states, the four-sublattice ordered state defined by the cubic unit cell of the fcc lattice. Due to geometrical constraints, flavor waves interact along specific planes only, thus rendering the system effectively two dimensional and forbidding ordering at finite temperatures. We argue that longer range interactions generated by quantum fluctuations can shift the transition to finite temperatures.