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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 \u03bb<\/mml:mi>\u03d5<\/mml:mi>4<\/mml:mn><\/mml:msup><\/mml:math> theory for benchmark, we evaluate the order \u03bb<\/mml:mi><\/mml:math> 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.<\/jats:p>","DOI":"10.22331\/q-2021-11-23-586","type":"journal-article","created":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T16:52:17Z","timestamp":1637686337000},"page":"586","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Tensor Renormalization Group for interacting quantum fields"],"prefix":"10.22331","volume":"5","author":[{"given":"Manuel","family":"Campos","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica Te\u00f3rica UAM\/CSIC, C\/ Nicol\u00e1s Cabrera 13-15, Cantoblanco, 28049 Madrid, Spain"}]},{"given":"German","family":"Sierra","sequence":"additional","affiliation":[]},{"given":"Esperanza","family":"Lopez","sequence":"additional","affiliation":[]}],"member":"9598","published-online":{"date-parts":[[2021,11,23]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"M. 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