2010/11/10 by M. D. Girardeau, Girardeau, M. D.
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #Quantum many-body systems #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1011.2514
openalex publication_date 2010/11/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Motivated by previous suggestions that three-body hard-core interactions in lower-dimensional ultracold Bose gases might provide a way for creation of non-Abelian anyons, the exact ground state of a harmonically trapped 1D Bose gas with three-body hard-core interactions is constructed by duality mapping, starting from an N-particle ideal gas of mixed symmetry with three-body nodes, which has double occupation of the lowest harmonic oscillator orbital and single occupation of the next N-2 orbitals. It has some similarity to the ground state of a Tonks-Girardeau gas, but is more complicated. It is proved that in 1D any system of N≥ 3 bosons with three-body hard-core interactions also has two-body soft-core interactions of generalized Lieb-Liniger delta function form, as a consequence of the topology of the configuration space of N particles in 1D, i.e., wave functions with only three-body hard core zeroes are topologically impossible. This is in contrast with the case of 2D, where pure three-body hard-core interactions do exist, and are closely related to the fractional quantized Hall effect. The exact ground state is compared with a previously-proposed Pfaffian-like approximate ground state, which satisfies the three-body hard-core constraint but is not an exact energy eigenstate. Both the exact ground state and the Pfaffian-like approximation imply two-body soft-core interactions as well as three-body hard-core interactions, in accord with the general topological proof.