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Long-range interactions in the quantum many-body problem in one dimension: ground state.
1Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India. saugata@prl.ernet.in
Summary
We studied N-body systems with unique interactions, finding their ground state energy resembles free fermions. The long-range interaction causes particle arrangement in bands and alters pair correlation functions compared to the Calogero-Sutherland model.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter theory
Background:
- The Calogero-Sutherland model (CSM) describes interacting particles in one dimension.
- Understanding N-body systems with complex potentials and interactions is crucial.
Purpose of the Study:
- Investigate ground state properties of N-body systems with polynomial potentials and long-range interactions.
- Compare these properties to the established Calogero-Sutherland model.
Main Methods:
- Analytical derivation of the Hamiltonian for the N-body system.
- Utilizing random matrix theory to analyze particle density and pair correlation functions.
- Solving for the ground state wave function.
Main Results:
- Ground state energy shows similarity to free fermions in a harmonic well.
- Energy displacement depends on particle number and potential depth.
- Particles arrange into distinct bands.
- Pair correlation function deviates from CSM due to long-range interactions.
Conclusions:
- The studied systems exhibit unique ground state properties influenced by long-range interactions.
- The findings offer insights into quantum systems beyond the standard Calogero-Sutherland model.
- Particle banding and altered correlations highlight the impact of interaction range.