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Back and forth from Fock space to Hilbert space: A guide for commuters

By A. Beggi, I. Siloi, C. Benedetti, E. Piccinini, L. Razzoli, P. Bordone and M.G.A. Paris

Abstract

Quantum states of systems made of many identical particles, e.g. those described by Fermi-Hubbard and Bose-Hubbard models, are conveniently depicted in the Fock space. However, in order to evaluate some specific observables or to study system dynamics, it is often more effective to employ the Hilbert space description. Moving effectively from one description to the other is thus a desirable feature, especially when a numerical approach is needed. Here we recall the construction of the Fock space for systems of indistinguishable particles, and then present a set of recipes and advice for students and researchers with the need to commute back and forth from one description to the other. The two-particle case is discussed in some detail, and a few guidelines for numerical implementations are given

Topics: Fock space, Hilbert space, identical particles, Physics and Astronomy (all), Settore FIS/03 - Fisica della Materia, Settore FIS/08 - Didattica e Storia della Fisica
Publisher: 'IOP Publishing'
Year: 2018
DOI identifier: 10.1088/1361-6404/aad760
OAI identifier: oai:air.unimi.it:2434/605358

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