Investigation of complex $\phi^{4}$ theory at finite density in two dimensions using TRG

TL;DR

This paper uses tensor renormalization group methods to study the complex $\

Contribution

It demonstrates the effectiveness of TRG in analyzing the complex $\

Findings

Silver Blaze phenomenon confirmed at large volume

TRG approach free from sign problem

Results validated by character expansion

Abstract

We study the two-dimensional complex $\phi^{4}$ 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 $V=1024^2$ and the results are also ensured by another tensor network representation with a character expansion.