# Towards quantum computing for the classical $O(2)$ model

Event Details

## Event Dates:

Tuesday, March 4, 2014 - 4:00pm

## Seminar Location:

• Duane Physics Room D142

## Speaker Name(s):

Prof. Yannick Meurice

## Speaker Affiliation(s):

University of Iowa
Seminar Type/Subject

• Other

## Seminar Type Other:

HIgh-enegy Physics Seminar

## Event 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.