Exact solution for the degenerate groundstate manifold of a strongly interacting onedimensional BoseFermi mixture
Abstract
We present the exact solution for the manybody wavefunction of a onedimensional mixture of bosons and spinpolarized 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 BoseFermi mapping, we find the solution for the whole set of groundstate wave functions of the degenerate manifold and we characterize them according to groupsymmetry 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 strongcoupling form of the BetheAnsatz solution for the homogeneous system, we propose an analytic expression for the manybody 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:

 Department of Physics, Block S12, Faculty of Science, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore)
 Universite de NiceSophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F06560 Valbonne (France)
 Universite Grenoble 1, CNRS, LPMMC, UMR5493, Maison des Magisteres, F38042 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 10502947
 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; MANYBODY PROBLEM; ONEDIMENSIONAL CALCULATIONS; SPIN ORIENTATION; STRONGCOUPLING 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 NiceSophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F06560 Valbonne, and Minguzzi, Anna. Exact solution for the degenerate groundstate manifold of a strongly interacting onedimensional BoseFermi 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 NiceSophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F06560 Valbonne, & Minguzzi, Anna. Exact solution for the degenerate groundstate manifold of a strongly interacting onedimensional BoseFermi 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 NiceSophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F06560 Valbonne, and Minguzzi, Anna. Mon .
"Exact solution for the degenerate groundstate manifold of a strongly interacting onedimensional BoseFermi mixture". United States. https://doi.org/10.1103/PHYSREVA.84.023626.
@article{osti_22068530,
title = {Exact solution for the degenerate groundstate manifold of a strongly interacting onedimensional BoseFermi 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 NiceSophia Antipolis, Institut Non Lineaire de Nice, CNRS, 1361 route des Lucioles, F06560 Valbonne and Minguzzi, Anna},
abstractNote = {We present the exact solution for the manybody wavefunction of a onedimensional mixture of bosons and spinpolarized 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 BoseFermi mapping, we find the solution for the whole set of groundstate wave functions of the degenerate manifold and we characterize them according to groupsymmetry 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 strongcoupling form of the BetheAnsatz solution for the homogeneous system, we propose an analytic expression for the manybody 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 = {10502947},
number = 2,
volume = 84,
place = {United States},
year = {2011},
month = {8}
}