Tensor Renormalization Group for interacting quantum fields

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...

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Autores principales:	Manuel Campos, German Sierra, Esperanza Lopez
Formato:	article
Lenguaje:	EN
Publicado:	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/b956eb1779684996b09dec955cf515c4
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id	oai:doaj.org-article:b956eb1779684996b09dec955cf515c4
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spelling	oai:doaj.org-article:b956eb1779684996b09dec955cf515c42021-11-23T16:36:03ZTensor Renormalization Group for interacting quantum fields2521-327X10.22331/q-2021-11-23-586https://doaj.org/article/b956eb1779684996b09dec955cf515c42021-11-01T00:00:00Zhttps://quantum-journal.org/papers/q-2021-11-23-586/pdf/https://doaj.org/toc/2521-327XWe 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.Manuel CamposGerman SierraEsperanza LopezVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenarticlePhysicsQC1-999ENQuantum, Vol 5, p 586 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Manuel Campos German Sierra Esperanza Lopez Tensor Renormalization Group for interacting quantum fields
description	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.
format	article
author	Manuel Campos German Sierra Esperanza Lopez
author_facet	Manuel Campos German Sierra Esperanza Lopez
author_sort	Manuel Campos
title	Tensor Renormalization Group for interacting quantum fields
title_short	Tensor Renormalization Group for interacting quantum fields
title_full	Tensor Renormalization Group for interacting quantum fields
title_fullStr	Tensor Renormalization Group for interacting quantum fields
title_full_unstemmed	Tensor Renormalization Group for interacting quantum fields
title_sort	tensor renormalization group for interacting quantum fields
publisher	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
publishDate	2021
url	https://doaj.org/article/b956eb1779684996b09dec955cf515c4
work_keys_str_mv	AT manuelcampos tensorrenormalizationgroupforinteractingquantumfields AT germansierra tensorrenormalizationgroupforinteractingquantumfields AT esperanzalopez tensorrenormalizationgroupforinteractingquantumfields
_version_	1718416234232414208

Tensor Renormalization Group for interacting quantum fields

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