Investigation of Complex ϕ4 Theory at Finite Density in Two Dimensions Using TRG

We study the two-dimensional complex ϕ4 theory at finite chemical potential using the tensor renormalization group. This model exhibits the Silver Blaze phenomenon in which bulk observables are independent of the chemical potential below the critical point. Since it is expected to be a direct outcome of an imaginary part of the action, an approach free from the sign problem is needed. We study this model systematically changing the chemical potential in order to check the applicability of the tensor renormalization group to the model in which scalar fields are discretized by the Gaussian quadrature. The Silver Blaze phenomenon is successfully confirmed on the extremely large volume V = 10242 and the results are also ensured by another tensor network representation with a character expansion.