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

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We have applied the TRG method to study the 2D pure U(1) gauge theory with a θ term.

The continuous degrees of freedom are discretized with the Gauss quadrature method. We

have confirmed that this model has a first-order phase transition at θ = π as predicted

from the analytical calculation. The successful analysis of the model demonstrates an effectiveness of the Gauss quadrature approach to the gauge theories. It should be interesting

to apply the TRG-based methods with the Gauss quadrature to higher dimensional gauge

theories with θ term which have been hardly investigated by the Monte Carlo approach

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