Variational Bethe Ansatz approach for dipolar one-dimensional bosons
arXiv:1910.05965 · doi:10.1103/PhysRevB.101.045102
Abstract
We propose a variational approximation to the ground state energy of a one-dimensional gas of interacting bosons on the continuum based on the Bethe Ansatz ground state wavefunction of the Lieb-Liniger model. We apply our variational approximation to a gas of dipolar bosons in the single mode approximation and obtain its ground state energy per unit length. This allows for the calculation of the Tomonaga-Luttinger exponent as a function of density and the determination of the structure factor at small momenta. Moreover, in the case of attractive dipolar interaction, an instability is predicted at a critical density, which could be accessed in lanthanide atoms.
12 pages, RevTex 4 (v1) references added (v2)
References in corpus (20)
- Bose-Einstein Condensation of Erbium
- Quantum-fluctuation-driven crossover from a dilute Bose-Einstein condensate to a macro-droplet in a dipolar quantum fluid
- Quantum degenerate dipolar Fermi gas
- Fractional Quantum Hall Effect in Optical Lattices
- Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
- Dynamical density-density correlations in the one-dimensional Bose gas
- Dipolar gases in quasi one-dimensional geometries
- Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
- Novel quantum phases of dipolar Bose gases in optical lattices
- Magnetic dipolar interaction in an atomic Bose Einstein condensate interferometer
- Evidence of Luttinger liquid behavior in one-dimensional dipolar quantum gases
- 1D Quantum Liquids with Power-Law Interactions: a Luttinger Staircase with Polar Molecules
- Superfluid to Mott-insulator transition in Bose-Hubbard models
- Successes and failures of Bethe Ansatz Density Functional Theory
- Two interacting fermions in a 1D harmonic trap: matching the Bethe ansatz and variational approaches
- The low-energy excitation spectrum of one-dimensional dipolar quantum gases
- Competition between Bose Einstein Condensation and spin dynamics
- Off-diagonal Ground State Properties of a 1D Gas of Fermi Hard Rods
- A variational method for integrability-breaking Richardson-Gaudin models
- Collective modes of a trapped Lieb-Liniger gas: a hydrodynamic approach