Tensor renormalization group approach to four-dimensional complex ${\varphi }^4$ theory at finite density

Abstract

Tensor network is an attractive approach to field theory with negative sign problem. The complex ${\varphi }^4$ theory at finite density is a test bed for numerical algorithms to verify their effectiveness. The model shows a characteristic feature called the Silver Blaze phenomenon associated with the sign problem in the large volume limit at low temperature. We analyze the four-dimensional model employing the anisotropic tensor renormalization group algorithm. We find a clear signal of the Silver Blaze phenomenon on a large volume of $V=1024^4$, which implies that the tensor network approach is effective even for four-dimensional field theory beyond two dimensions.

11 pages, 6 figures

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Cited by in corpus (4)

• Tensor renormalization group study of (3+1)-dimensional $Z_2$ gauge-Higgs model at finite density
• Tensor renormalization group approach to (1+1)-dimensional Hubbard model
• Tensor renormalization group study of (1+1)-dimensional U(1) gauge-Higgs model at $\theta =\pi$ with Lüscher's admissibility condition
• Applying the Triad network representation to four-dimensional ATRG method