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A quantum Mermin-Wagner theorem for a generalized Hubbard model

Advances in mathematical physics. 2013. Vol. 2013.
Kelbert M., Suhov Y.

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.

Priority areas: mathematics
Language: English
Full text
Keywords: Habbard modelMermin-Wagner theoremquantum oscillatorмодель Хаббардтеорема Мермина-Вагнераквантовый осцилятор
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