2015/02/03 by Stefan S. Natu, J. H. Pixley, S. Das Sarma
Physics and Astronomy · #Boson #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Effective field theory #Excited state #Ferromagnetism #Goldstone boson #Mean field theory #Mott insulator #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Quantum, superfluid, helium dynamics #Quasiparticle #Singlet state #Spin wave #Superconductivity #Superfluidity #cond-mat.quant-gas #quant-ph
paper · pdf · doi:10.1103/physreva.91.043620
published as Phys. Rev. A 91 043620 (2015) · 12 pages, 6 figures
arxiv created 2015/02/03 · openalex publication_date 2015/04/14 · arxiv updated 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the physics of interacting spin-1 bosons in an optical lattice using a variational Gutzwiller technique. We compute the mean-field ground state wave function and discuss the evolution of the condensate, spin, nematic, and singlet order parameters across the superfluid-Mott transition. We then extend the Gutzwiller method to derive the equations governing the dynamics of low energy excitations in the lattice. Linearizing these equations, we compute the excitation spectra in the superfluid and Mott phases for both ferromagnetic and antiferromagnetic spin-spin interactions. In the superfluid phase, we recover the known excitation spectrum obtained from Bogoliubov theory. In the nematic Mott phase, we obtain gapped, quadratically dispersing particle and hole-like collective modes, whereas in the singlet Mott phase, we obtain a nondispersive gapped mode, corresponding to the breaking of a singlet pair. For the ferromagnetic Mott insulator, the Gutzwiller mean-field theory only yields particle-hole-like modes but no Goldstone mode associated with long-range spin order. To overcome this limitation, we supplement the Gutzwiller theory with a Schwinger boson mean-field theory which captures superexchange-driven fluctuations. In addition to the gapped particle-hole-like modes, we obtain a gapless quadratically dispersing ferromagnetic spin-wave Goldstone mode. We discuss the evolution of the singlet gap, particle-hole gap, and the effective mass of the ferromagnetic Goldstone mode as the superfluid-Mott phase boundary is approached from the insulating side. We discuss the relevance and validity of Gutzwiller mean-field theories to spinful systems, and potential extensions of this framework to include more exotic physics which appears in the presence of spin-orbit coupling or artificial gauge fields.