Symmetry reduction of tensor networks in many-body theory I. Automated symbolic evaluation of $SU(2)$ algebra

Autor: R. Wirth, Thomas Duguet, J. Ripoche, Alexander Tichai
Přispěvatelé: Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)
Rok vydání: 2020
Předmět:
Zdroj: European Physical Journal A
European Physical Journal A, EDP Sciences, 2020, 56 (10), pp.272. ⟨10.1140/epja/s10050-020-00233-6⟩
Eur.Phys.J.A
Eur.Phys.J.A, 2020, 56 (10), pp.272. ⟨10.1140/epja/s10050-020-00233-6⟩
ISSN: 1434-6001
1434-601X
DOI: 10.48550/arxiv.2002.05011
Popis: 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 Schr\"odinger 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 angular-momentum, i.e. $SU(2)$, quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone 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 angular-momentum reduction is presented. Taking the symmetry-unrestricted 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 demonstrate the generality of the approach and to highlight the potential impact on the many-body community.
Comment: 24 pages, 4 figures, accompanying source code available at github.com/radnut/amc
Databáze: OpenAIRE
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