Exactly Solvable System of One-Dimensional Trapped Bosons with Short- and Long-Range Interactions.

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Many-body systems

Background:

• Understanding the behavior of interacting quantum particles is crucial in condensed matter physics.
• Trapped bosons exhibit complex phases depending on interaction types and strengths.

Purpose of the Study:

• To develop and analyze a model for one-dimensional trapped bosons with contact interactions and either Coulomb repulsion or gravitational attraction.
• To determine the exact ground-state energy and many-body wave function for the system.
• To investigate the density profile and pair-correlation function across various interaction regimes.

Main Methods:

• Analytical derivation of the exact ground-state energy and many-body wave function.
• Monte Carlo sampling to analyze the density profile and pair-correlation function.
• Comparison with theoretical models like Gross-Pitaevskii equation for specific regimes.

Main Results:

• The model exhibits diverse physical regimes, including quantum solitons under strong attraction.
• Weak repulsion leads to a Laughlin-like incompressible fluid, accurately described by Gross-Pitaevskii theory.
• Increased repulsion drives Friedel oscillations and the formation of a Wigner crystal.

Conclusions:

• The study provides an exact solution for a complex boson system, revealing rich emergent phenomena.
• The findings highlight the significant impact of interaction types (attraction vs. repulsion) on the system's phase diagram.
• The model serves as a valuable tool for understanding quantum many-body physics in one dimension.