Antiferroquadrupolar order and rotational symmetry breaking in a generalized bilinear-biquadratic model on a square lattice

TL;DR

This paper investigates a generalized bilinear-biquadratic model on a square lattice, revealing a stable antiferroquadrupolar phase with C4 symmetry breaking, supported by numerical methods, and discusses implications for iron-based superconductors like FeSe.

Contribution

It identifies and characterizes a large parameter regime of antiferroquadrupolar order stabilized by quantum fluctuations, providing new insights into nematic phases in iron chalcogenides.

Findings

Discovery of a stable antiferroquadrupolar phase in the model.

Quantum fluctuations lift degeneracy, stabilizing the phase.

Evidence from density matrix renormalization group analysis.

Abstract

The magnetic and nematic properties of the iron chalcogenides have recently been the subject of intense interest. Motivated by the proposed antiferroquadrupolar and Ising-nematic orders for the bulk FeSe, we study the phase diagram of an $S=1$ generalized bilinear-biquadratic model with multi-neighbor interactions. We find a large parameter regime for a ($\pi$,0) antiferroquadrupolar phase, showing how quantum fluctuations stabilize it by lifting an infinite degeneracy of certain semiclassical states. Evidence for this C$_4$-symmetry-breaking quadrupolar phase is also provided by an unbiased density matrix renormalization group analysis. We discuss the implications of our results for FeSe and related iron-based superconductors.