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Strongly interacting confined quantum systems in one dimension.

A G Volosniev1, D V Fedorov1, A S Jensen1

  • 1Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, Aarhus C DK-8000, Denmark.

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|November 5, 2014
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This study introduces a new technique to solve one-dimensional (1D) quantum systems with strong interactions. It reveals the presence of both ferromagnetic and antiferromagnetic states in small systems, enabling quantum manipulation of magnetic correlations.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Atomic physics

Background:

  • The study of one-dimensional (1D) magnetism has a long history, dating back to Bethe's solution of the Heisenberg model.
  • Recent advances in cold atomic gases have led to the realization of 1D systems, such as the Tonks-Girardeau gas, making them a forefront research area.
  • Understanding quantum behavior in 1D systems is crucial for developing new quantum technologies.

Purpose of the Study:

  • To develop a new method for solving 1D fermionic and bosonic systems with strong short-range interactions.
  • To obtain the full spectrum of energies and eigenstates for these systems in arbitrary confining geometries.
  • To investigate the emergence of magnetic correlations in small 1D systems relevant to current experiments.

Main Methods:

  • Introduction of a novel energy-functional technique.
  • Analytical solution for 1D quantum systems with strong short-range interactions.
  • Calculation of spatial correlations to identify magnetic states.

Main Results:

  • The developed method successfully solves 1D fermionic and bosonic systems in arbitrary confining geometries.
  • The full spectrum of energies and eigenstates for these systems has been obtained.
  • Both ferro- and antiferromagnetic states are shown to be present even for small system sizes.

Conclusions:

  • The new energy-functional technique provides a powerful tool for studying 1D quantum magnetism.
  • The findings demonstrate the feasibility of preparing and studying magnetic correlations at the microscopic scale in current experimental setups.
  • This work highlights the significant potential for quantum manipulation of magnetic correlations in 1D systems.