Natural generalization of the ground-state Slater determinant to more than one dimension

Sunko, Denis (2016) Natural generalization of the ground-state Slater determinant to more than one dimension. Physical Review A, 93 (6). pp. 62109-13. ISSN 1050-2947

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Abstract

The basic question is addressed of how the space dimension d is encoded in the Hilbert space of N identical fermions. There appears a finite number N!^(d−1) of many-body wave functions, called shapes, which cannot be generated by trivial combinatorial extension of the one-dimensional ones. A general algorithm is given to list them all in terms of standard Slater determinants. Conversely, excitations which can be induced from the one-dimensional case are bosonized into a system of distinguishable bosons, called Euler bosons, much like the electromagnetic field is quantized in terms of photons distinguishable by their wave numbers. Their wave functions are given explicitly in terms of elementary symmetric functions, reflecting the fact that the fermion sign problem is trivial in one dimension. The shapes act as vacua for the Euler bosons. They are the natural generalization of the single-Slater-determinant form for the ground state to more than one dimension. In terms of algebraic invariant theory, the shapes are antisymmetric invariants which finitely generate the N-fermion Hilbert space as a graded algebra over the ring of symmetric polynomials. Analogous results hold for identical bosons.

Item Type: Article
Keywords: many-body wave functions, fermion sign problem, graded algebra
Date: 7 June 2016
Subjects: NATURAL SCIENCES > Physics
Additional Information: © 2016 American Physical Society. Received 10 December 2015; revised manuscript received 12 February 2016; published 7 June 2016.
Divisions: Faculty of Science > Department of Physics
Project code: 202759, 119-1191458-0512
Funders: Ministarstvo znanosti, obrazovanja i športa
Publisher: American Physical Society
Depositing User: Gordana Stubičan Ladešić
Date Deposited: 13 Jul 2016 11:21
Last Modified: 13 Jul 2016 11:21
URI: http://digre.pmf.unizg.hr/id/eprint/4968

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