Event DetailsEvent Dates: Tuesday, March 4, 2014 - 4:00pmSeminar Location: Duane Physics Room D142Speaker Name(s): Prof. Yannick Meurice Speaker Affiliation(s): University of Iowa Seminar Type/SubjectScientific Seminar Type: OtherSeminar Type Other: HIgh-enegy Physics SeminarEvent Details & Abstract: The classical $O(2)$ model on an isotropic Euclidean space-time lattice has many common features with the models studied by lattice gauge theorists. The continuum limit in the time direction leads to an Hamiltonian describing coupled abelian rotors on a space lattice. When a large chemical potential is introduced, it is possible to qualitatively map the abelian rotor model into a Bose-Hubbard model. We use the tensor renormalization group (TRG) formulation of the classical nonlinear sigma $O(2)$ model with time link couplings $\beta_t$, space link coupling $\beta_x$ and a chemical potential $\mu$ to show that this qualitative picture is quantitatively correct. We map the phase diagrams of the isotropic $\beta_t =\beta_x$ and the time continuum limit $\beta_t >>\beta_x$ into each other and with the Bose-Hubbard model by a change of coordinates in the $\beta-\mu$ plane. We check our numerical results with the worm algorithm at small volume. We discuss the possibility of constructing Bose-Hubbard models that can describe the isotropic $O(2)$ model on an isotropic Euclidean lattice and without chemical potential.