A quantum Mermin--Wagner theorem for a generalized Hubbard model on a 2D graph

Abstract

This paper is the second in a series of papers considering symmetry properties of a bosonic quantum system over an 2D graph, with continuous spins, in the spirit of the Mermin--Wagner theorem. Here we consider bosonic systems on bi-dimensional graphs where particles can jump from a vertex to another (a generalized Hubbard model). The Feynman--Kac representation is used for proving that if the local Hamiltonians are invariant under a continuous group of transformations $\mathtt{G}$ (a Euclidean space or a torus of dimension $d^{\prime }$ acting on a torus of dimension $d\ge d^{\prime }$) then any infinite-volume Gibbs state from a certain class (introduced in the paper) is also $\mathtt{G}$-invariant.

48 pages

References in corpus (4)

• A Mermin--Wagner theorem on Lorentzian triangulations with quantum spins
• A quantum Mermin--Wagner theorem for quantum rotators on two--dimensional graphs
• Shift-invariance for FK-DLR states of a 2D quantum bose-gas
• A Mermin--Wagner theorem for Gibbs states on Lorentzian triangulations

Cited by in corpus (4)

• A Mermin--Wagner theorem on Lorentzian triangulations with quantum spins
• A quantum Mermin--Wagner theorem for quantum rotators on two--dimensional graphs
• FK-DLR states of a quantum bose-gas with a card-core interaction
• FK-DLR properties of a quantum multi-type bose-gas with a repulsive interaction