Magnetically Stabilized Nematic Order I: Three-Dimensional Bipartite Optical Lattices

TL;DR

This paper investigates how magnetic fields induce nematic order in spin-one bosons on 3D bipartite optical lattices, revealing quantum phase transitions and critical behaviors linked to magnon condensation.

Contribution

It provides a microscopic understanding of magnetically stabilized nematic order and characterizes the quantum phase transitions as magnon condensations in a 3D bipartite lattice.

Findings

Quantum transitions are in the ferromagnetic XXZ universality class.

Nematic order develops via magnon condensation breaking U(1) symmetry.

Quadratic Zeeman effects induce Ising nematic order.

Abstract

We study magnetically stabilized nematic order for spin-one bosons in optical lattices. We show that the Zeeman field-driven quantum transitions between non-nematic Mott states and quantum spin nematic states in the weak hopping limit are in the universality class of the ferromagnetic XXZ (S=1/2) spin model. We further discuss these transitions as condensation of interacting magnons. The development of O(2) nematic order when external fields are applied corresponds to condensation of magnons, which breaks a U(1) symmetry. Microscopically, this results from a coherent superposition of two non-nematic states at each individual site. Nematic order and spin wave excitations around critical points are studied and critical behaviors are obtained in a dilute gas approximation. We also find that spin singlet states are unstable with respect to quadratic Zeeman effects and Ising nematic order appears in the presence of any finite quadratic Zeeman coupling. All discussions are carried out for states in three dimensional bipartite lattices.