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

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 Hilber...

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Bibliographic Details
Published in:European journal of physics 2018-11, Vol.39 (6), p.65401
Main Authors: Beggi, Andrea, Siloi, Ilaria, Benedetti, Claudia, Piccinini, Enrico, Razzoli, Luca, Bordone, Paolo, Paris, Matteo G A
Format: Article
Language:English
Subjects:
Fock space
Hilbert space
identical particles
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Summary: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.
ISSN:0143-0807
1361-6404
DOI:10.1088/1361-6404/aad760