Ground States of the Spin-1 Bose-Hubbard Model

Abstract

We prove basic theorems about the ground states of the S=1 Bose-Hubbard model. The results are quite universal and depend only on the coefficient U_2 of the spin-dependent interaction. We show that the ground state exhibits saturated ferromagnetism if U_2<0, is spin-singlet if U_2>0, and exhibits "SU(3)-ferromagnetism" if U_2=0, and completely determine the degeneracy in each region.

arXiv comment5 pages, no figures, version 2: small changes, one reference is added

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Cited by in corpus (20)

• Ultracold bosons with short-range interaction in regular optical lattices
• Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect
• Interacting spin-1 bosons in a two-dimensional optical lattice
• Static and Dynamic Properties of Interacting Spin-1 Bosons in an Optical Lattice
• Anderson tower of states and nematic order of spin-1 bosonic atoms on a 2D lattice
• Quantum magnetism of ultracold atoms with a dynamical pseudospin degree of freedom
• Ground-state entanglement of spin-1 bosons undergoing superexchange interactions in optical superlattices
• Symmetry-protected Topological Phases in Spinful Bosons with a Flat Band
• Mott lobes of the $S=1$ Bose-Hubbard model with three-body interactions
• Analysis and resolution of the ground-state degeneracy of the two-component Bose-Hubbard model
• "Polar" and "antiferromagnetic" order in f=1 many-boson systems
• Phase Diagrams of Antiferromagnetic Spin-1 Bosons on Square Optical Lattice with the Quadratic Zeeman Effect
• Strongly Spinor Ferromagnetic Bose Gases
• Phase diagrams and multistep condensations of spin-1 bosonic gases in optical lattices
• Upper bound of one-magnon excitation and lower bound of effective mass for ferromagnetic spinor Bose and Fermi gases
• Rigorous Results for the Ground States of the Spin-2 Bose-Hubbard Model
• Phase transitions and spin excitations of spin-1 bosons in optical lattice
• Spin-1 Bose-Hubbard model with two- and three-body interactions
• Spinor Bose gas in an elongated trap
• Strong-coupling study of spin-1 bosons in square and triangular optical lattice