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

11 pages, 9 figures

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• Density Matrix Renormalization Group Study of Nematicity in Two Dimensions: Application to a Spin-$1$ Bilinear-Biquadratic Model on the Square Lattice

Cited by in corpus (8)

• On the Remarkable Superconductivity of FeSe and its Close Cousins
• Magnetic Topological Semimetal Phase with Electronic Correlation Enhancement in SmSbTe
• Lattice-Shifted Nematic Quantum Critical Point in FeSe${}_{1-x}$S${}_x$
• Evolution of Electronic and Magnetic Properties in Topological Semimetal SmSbxTe2-x
• Range of biquadratic and triquadratic Heisenberg effective couplings deduced from multiorbital Hubbard models
• Field-induced spin nematic Tomonaga-Luttinger liquid of the $S=1/2$ spin ladder system with the anisotropic ferromagnetic rung interaction
• Stronger quantum fluctuation with larger spins: Emergent magnetism in the pressurized high-temperature superconductor FeSe
• Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model