Quantum Transitions of Nematic Phases in a Spin-$1$ Bilinear-Biquadratic Model and Their Implications for FeSe

TL;DR

This paper models the nematic phases in FeSe using a quantum spin model, revealing phase transitions and exotic orders that could explain experimental observations and suggest a magnetic origin for superconductivity.

Contribution

It introduces a spin-$1$ bilinear-biquadratic model analysis with DMRG to explain nematic phases in FeSe, linking quantum transitions to experimental findings.

Findings

Identified quantum transitions from antiferromagnetic to antiferroquadrupolar order.

Revealed all phases are nematic, consistent with experimental observations.

Proposed a magnetic-based explanation for superconductivity in FeSe.

Abstract

Since its discovery, iron-based superconductivity has been known to develop near an antiferromagnetic order, but this paradigm fails in the iron chalcogenide FeSe, whose single-layer version holds the record for the highest superconducting transition temperature in the iron-based superconductors. The striking puzzle that FeSe displays nematic order (spontaneously broken lattice rotational symmetry) while being non-magnetic, has led to several competing proposals for its origin in terms of either the $3d$-electron's orbital degrees of freedom or spin physics in the form of frustrated magnetism. Here we argue that the phase diagram of FeSe under pressure could be qualitatively described by a quantum spin model with highly frustrated interactions. We implement both the site-factorized wave-function analysis and the large-scale density matrix renormalization group (DMRG) in cylinders to study the spin-$1$ bilinear-biquadratic model on the square lattice, and identify quantum transitions from the well-known $(\pi,0)$ antiferromagnetic state to an exotic $(\pi,0)$ antiferroquadrupolar order, either directly or through a $(\pi/2,\pi)$ antiferromagnetic state. These many phases, while distinct, are all nematic. We also discuss our theoretical ground-state phase diagram for the understanding of the experimental low-temperature phase diagram obtained by the NMR [P. S. Wang {\it et al.}, Phys. Rev. Lett. 117, 237001 (2016)] and X-ray scattering [K. Kothapalli {\it et al.}, Nature Communications 7, 12728 (2016)] measurements in pressurized FeSe. Our results suggest that superconductivity in a wide range of iron-based materials has a common origin in the antiferromagnetic correlations of strongly correlated electrons.