Rigorous Results for the Ground States of the Spin-2 Bose-Hubbard Model
ORAL
Abstract
In this work, we prove rigorous theorems for the ground states of the spin-2 Bose-Hubbard model, concerning the magnetic properties, degeneracies and forms of the wave functions. The theorems are highly universal in the sense that they do not depend on the lattice structure (including spatial dimension), particle number and spin-independent interaction.
The spin-2 Bose-Hubbard model is a model for ultracold f = 2 spinor bosonic atoms in optical lattices. We prove that, with c1 and c2 being the coefficients of the two spin-dependent interaction terms of the Hamiltonian, the ground state has a maximum total spin when c1 < 0 and c2 ≧ 5c1, while tends to be a singlet if c1 = 0 and c2 < 0. When c1 = c2 = 0, the model has SU(5) symmetry. Furthermore, the ground-state degeneracies and the forms of wave function are also exactly determined in each coefficient region. Our approach takes the advantage of the symmetry of the Hamiltonian and employs sophisticated mathematical tools including the Perron-Frobenius theorem and the min-max theorem, as well as the representation theory of so(5) Lie algebra.
References
[1] Hong Yang and Hosho Katsura. arXiv:1803.09441 (2018).
[2] M. Koashi and M. Ueda, Phys. Rev. Lett. 84, 1066 (2000).
[3] M. Ueda and M. Koashi, Phys. Rev. A 65, 063602 (2002).
The spin-2 Bose-Hubbard model is a model for ultracold f = 2 spinor bosonic atoms in optical lattices. We prove that, with c1 and c2 being the coefficients of the two spin-dependent interaction terms of the Hamiltonian, the ground state has a maximum total spin when c1 < 0 and c2 ≧ 5c1, while tends to be a singlet if c1 = 0 and c2 < 0. When c1 = c2 = 0, the model has SU(5) symmetry. Furthermore, the ground-state degeneracies and the forms of wave function are also exactly determined in each coefficient region. Our approach takes the advantage of the symmetry of the Hamiltonian and employs sophisticated mathematical tools including the Perron-Frobenius theorem and the min-max theorem, as well as the representation theory of so(5) Lie algebra.
References
[1] Hong Yang and Hosho Katsura. arXiv:1803.09441 (2018).
[2] M. Koashi and M. Ueda, Phys. Rev. Lett. 84, 1066 (2000).
[3] M. Ueda and M. Koashi, Phys. Rev. A 65, 063602 (2002).
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Presenters
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Hong Yang
Department of Physics, The University of Tokyo
Authors
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Hong Yang
Department of Physics, The University of Tokyo
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Hosho Katsura
Physics, University of Tokyo, Department of Physics, University of Tokyo, University of Tokyo, Department of Physics, The University of Tokyo