Tensor Renormalization Group for interacting quantum fields

Manuel Campos; German Sierra; Esperanza Lopez

doi:10.22331/q-2021-11-23-586

Tensor Renormalization Group for interacting quantum fields

Manuel Campos¹, German Sierra, and Esperanza Lopez

¹Instituto de Física Teórica UAM/CSIC, C/ Nicolás Cabrera 13-15, Cantoblanco, 28049 Madrid, Spain

Published:	2021-11-23, volume 5, page 586
Eprint:	arXiv:2105.00010v3
Doi:	https://doi.org/10.22331/q-2021-11-23-586
Citation:	Quantum 5, 586 (2021).

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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.

Popular summary

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 previously 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.

► BibTeX data

@article{Campos2021tensor,
  doi = {10.22331/q-2021-11-23-586},
  url = {https://doi.org/10.22331/q-2021-11-23-586},
  title = {Tensor {R}enormalization {G}roup for interacting quantum fields},
  author = {Campos, Manuel and Sierra, German and Lopez, Esperanza},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {586},
  month = nov,
  year = {2021}
}

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