Exactly-solvable system of one-dimensional trapped bosons with short and long-range interactions
arXiv:2009.03319 · doi:10.1103/PhysRevLett.125.220602
Abstract
We consider trapped bosons with contact interactions as well as Coulomb repulsion or gravitational attraction in one spatial dimension. The exact ground state energy and wave function are identified in closed form together with a rich phase diagram, unveiled by Monte Carlo methods, with crossovers between different regimes. A trapped McGuire quantum soliton describes the attractive case. Weak repulsion results in an incompressible Laughlin-like fluid with flat density, well reproduced by a Gross-Pitaevskii equation with long-range interactions. Higher repulsion induces Friedel oscillation and the eventual formation of a Wigner crystal.
1 figure, 7 pages
References in corpus (5)
- The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
- Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
- Anyon-fermion mapping and applications to ultracold gases in tight waveguides
- Non Relativistic Limit of Integrable QFT and Lieb-Liniger Models
- Exact ground states of quantum many-body systems under confinement
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