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 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.
Highlights
IntroductionAb initio nuclear many-body theory has undergone a major renewal. In this process, expansion methods have become prominent in large-scale applications to mid-mass nuclei
In recent years, ab initio nuclear many-body theory has undergone a major renewal
Every member of the aforementioned approaches can be applied to much higher masses and larger system sizes than exact methods, the truncation levels needed for high-accuracy calculations require substantial effort in the derivation of the formalisms and for their numerical implementations
Summary
Ab initio nuclear many-body theory has undergone a major renewal. In this process, expansion methods have become prominent in large-scale applications to mid-mass nuclei. The success obtained within the last two decades is leading to the design of more and more advanced approaches to continuously refine the accuracy of the calculations and extend them systematically to an even larger portion of the nuclear chart This rise in the degree of sophistication of state-of-the-art many-body expansion schemes is leading to an increase of the formal complexity that is at the edge of what is humanly processable. Moving to the realm of medium- and heavy-mass nuclei involves the use of expansion many-body techniques building a wave-function parametrization on top of a conveniently chosen reference state These methods display a polynomial scaling with system size, the degree of the polynomial increasing with the targeted accuracy, i.e., with the order at which the expansion is truncated. Every member of the aforementioned approaches can be applied to much higher masses and larger system sizes than exact methods, the truncation levels needed for high-accuracy calculations require substantial effort in the derivation of the formalisms and for their numerical implementations
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