Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session M49: Precision Many-Body Physics V: New Algorithms
8:00 AM–11:00 AM,
Wednesday, March 16, 2022
Room: McCormick Place W-471B
Sponsoring Unit: DCOMP
Chair: Hansveer Singh, University of Massachusetts, Amherst
Abstract: M49.00004 : New formalism for the exact calculation of total energies and associated electronic states of many-body interactions with complexity n4
9:00 AM–9:12 AM
This formalism should considerably reduce the computation time avoiding the exponential complexity of the current exact methods. One can also ask the question of the interest of quantum computers if n4 parameters suffice to describe an intricate quantum experimental state.
Based on anti-commutativity relations, we show that we can construct a class of mathematical objects that are isomorphic to many-body wavefunctions but have the advantage of being compactable. Thanks to this new formalism, we show that the 2-RDM of the wavefunctions solutions of a two-body interaction Hamiltonian can be represented exactly thanks to this new set of mathematical objects. We will give also a new geometric interpretation of the 2-RDM in the space of these new mathematical objects.
We will develop the Lagrangian, the corresponding Euler-Lagrange equations and illustrate with numerical examples.
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