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.
Highlights
Understanding the iron-based superconductors (FeSCs) has been a subject of extensive research in recent years [1,2,3,4,5]
We focus on studying a spin-1 bilinear-biquadratic model on the square lattice, which has been considered before to understand the exotic magnetism and nematic order of the iron-chalcogenide superconductors [24,25,31,32,33,34,35,36] but has not been systematically studied to understand the quantum phases and phase transitions of FeSe under pressure
We find four stable spin dipolar and quadrupolar phases, including the Néel antiferromagnetic order, the (π, 0) collinear antiferromagnetic phase (CAFM), the (π /2, π ) antiferromagnetic phase (AFM*), and the (π, 0) antiferroquadrupolar phase (AFQ), and obtain the ground-state phase diagrams
Summary
Understanding the iron-based superconductors (FeSCs) has been a subject of extensive research in recent years [1,2,3,4,5]. We focus on studying a spin-1 bilinear-biquadratic model on the square lattice, which has been considered before to understand the exotic magnetism and nematic order of the iron-chalcogenide superconductors [24,25,31,32,33,34,35,36] but has not been systematically studied to understand the quantum phases and phase transitions of FeSe under pressure We implement both the site-factorized wave-function analysis and large-scale DMRG method on this model.
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