Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a θ term

Yoshinobu Kuramashi, Yusuke Yoshimura

Abstract We make an analysis of the two-dimensional U(1) lattice gauge theory with a θ term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling constant. The topological charge density generates a finite gap at θ = π toward the thermodynamic limit. In addition finite size scaling analysis of the topological susceptibility up to V = L × L = 1024 × 1024 allows us to determine the phase transition at θ = π is the first order.

Yusuke Yoshimura

S.J. Baker, R. F. Bishop, NEIL J. DAVIDSON

Shinichiro Akiyama, Y. Kuramashi, Yusuke Yoshimura

We report recent progress on the application of the tensor renormalization group (TRG) to quantum field theories pursued by the Tsukuba group. We explain how to treat the scalar, fermion, and gauge theories with the TRG method presenting the results for the phase transitions in the (3+1)-dimensional ((3+1)$d$) complex $\phi^4$ theory at finite density, (1+1)$d$ pure U(1) lattice gauge theory with a $\theta$ term, (3+1)$d$ Nambu--Jona-Lasinio model at finite density and (1+1)$d$ and (2+1)$d$ Hubbard models at an arbitrary chemical potential. It is demonstrated that the TRG method is free from the sign problem in practical calculations and applicable to the four-dimensional models.

D. Horn, Shimon Yankielowicz B

This study clarifies the phase structure of the two-dimensional lattice CP(1) model with a θ term by employing the tensor renormalization group method and conformal field theory, thus enabling the circumvention of the sign problem and logarithmic corrections.