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Title: Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture

Abstract

We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping, we find the solution for the whole set of ground-state wave functions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wave functions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system, we propose an analytic expression for the many-body wave function of the inhomogeneous system which well describes the ground state at finite, large, and equal interaction strengths, as validated by numerical simulations.

Authors:
 [1]; ;  [2];  [1];  [3]
  1. Department of Physics, Block S12, Faculty of Science, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore)
  2. Universite de Nice-Sophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F-06560 Valbonne (France)
  3. Universite Grenoble 1, CNRS, LPMMC, UMR5493, Maison des Magisteres, F-38042 Grenoble (France)
Publication Date:
OSTI Identifier:
22068530
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 2; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOSONS; COMPUTERIZED SIMULATION; EXACT SOLUTIONS; FERMIONS; GROUND STATES; MANY-BODY PROBLEM; ONE-DIMENSIONAL CALCULATIONS; SPIN ORIENTATION; STRONG-COUPLING MODEL; SYMMETRY; WAVE FUNCTIONS

Citation Formats

Fang, Bess, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Vignolo, Patrizia, Gattobigio, Mario, Miniatura, Christian, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Universite de Nice-Sophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F-06560 Valbonne, and Minguzzi, Anna. Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.023626.
Fang, Bess, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Vignolo, Patrizia, Gattobigio, Mario, Miniatura, Christian, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Universite de Nice-Sophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F-06560 Valbonne, & Minguzzi, Anna. Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture. United States. https://doi.org/10.1103/PHYSREVA.84.023626
Fang, Bess, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Vignolo, Patrizia, Gattobigio, Mario, Miniatura, Christian, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Universite de Nice-Sophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F-06560 Valbonne, and Minguzzi, Anna. Mon . "Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture". United States. https://doi.org/10.1103/PHYSREVA.84.023626.
@article{osti_22068530,
title = {Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture},
author = {Fang, Bess and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 and Vignolo, Patrizia and Gattobigio, Mario and Miniatura, Christian and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 and Universite de Nice-Sophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F-06560 Valbonne and Minguzzi, Anna},
abstractNote = {We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping, we find the solution for the whole set of ground-state wave functions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wave functions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system, we propose an analytic expression for the many-body wave function of the inhomogeneous system which well describes the ground state at finite, large, and equal interaction strengths, as validated by numerical simulations.},
doi = {10.1103/PHYSREVA.84.023626},
url = {https://www.osti.gov/biblio/22068530}, journal = {Physical Review. A},
issn = {1050-2947},
number = 2,
volume = 84,
place = {United States},
year = {2011},
month = {8}
}