Tensor Renormalization Group for interacting quantum fields

• URL: http://arxiv.org/abs/2105.00010v3
• Date: Wed, 17 Nov 2021 07:32:22 GMT
• Title: Tensor Renormalization Group for interacting quantum fields
• Authors: Manuel Campos, German Sierra, Esperanza Lopez
• Abstract summary: We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. We include an arbitrary self-interaction and treat it in the context of perturbation theory. The results show a fast convergence with the bond dimension, implying that our algorithm captures well the effect of interaction on entanglement.
• Score: 0.5801044612920815
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level of fields. This strategy was applied in Ref.[1] to the much simpler case of a free boson, obtaining an excellent performance. Here we include an arbitrary self-interaction and treat it in the context of perturbation theory. A real space analogue of the Wilsonian effective action and its expansion in Feynman graphs is proposed. Using a $\lambda \phi^4$ theory for benchmark, we evaluate the order $\lambda$ correction to the free energy. The results show a fast convergence with the bond dimension, implying that our algorithm captures well the effect of interaction on entanglement.

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