A quantum Mermin-Wagner theorem for a generalized Hubbard model
We study symmetry properties of bosonic quantum systems over 2D graphs, with
continuous spins, in the spirit of the Mermin-Wagner theorem. The Hamiltonian includes a kinetic part
responsible for the motion of a particle while “trapped” by a given atom, as well as a potential part. The system under consideration can be considered as a generalized (bosonic) Hubbard model. The result of the paper is that any (appropriately defined) Gibbs states generated by the above Hamiltonian preserves continuous symmetry,provided that the thermodynamic variables (the fugacity 𝑧 and the inverse temperature 𝛽) satisfy a certain restriction. The definition of a Gibbs state (and its analysis) is based on the Feynman-Kac representation for the density matrices.