Symmetry reduction of tensor networks in many-body theory
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Symmetry reduction of tensor networks in many-body theory I. Automated symbolic evaluation of SU (2) algebra A. Tichai1,2,3,4,a , R. Wirth5,b , J. Ripoche6,c , T. Duguet7,8,d 1
Max-Planck-Institut für Kernphysik, Heidelberg, Germany Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany 3 ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 4 ESNT, CEA-Saclay, DRF, IRFU, Département de Physique Nucléaire, Université de Paris Saclay, 91191 Gif-sur-Yvette, France 5 Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824, USA 6 CEA, DAM, DIF, 91297 Arpajon, France 7 IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France 8 KU Leuven, Instituut voor Kern- en Stralingsfysica, 3001 Leuven, Belgium
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Received: 12 February 2020 / Accepted: 22 July 2020 / Published online: 26 October 2020 © The Author(s) 2020 Communicated by Jerome Margueron
Abstract The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angularmomentum, i.e. SU (2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and errorprone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angularmomentum reduction is presented. Taking the symmetryunrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to a e-mail: author)
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demonstrate the generality of the approach and to highlight the potential impact on the many-body community.
PROGRAM SUMMARY Program title: AMC Licensing provisions: GNU General Public License Version 3 or later Programming language: Python 3 Repository and DOI: http://www.github.com/radnut/amc https://doi.org/10.5281/zenodo.3788328 Nature of problem: Numerical implementations of stateof-the-art many-body approaches require extensive use of angular-momentum algebra to derive the
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