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Antiferromagnetic spin-S chains with exactly dimerized ground states.

Frédéric Michaud1, François Vernay, Salvatore R Manmana

  • 1Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

Physical Review Letters
|May 1, 2012
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Summary

Spin S Heisenberg spin chains with a specific three-body interaction exhibit fully dimerized ground states. This finding generalizes the Majumdar-Ghosh point and has implications for antiferromagnetic chains.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Magnetism

Background:

  • Spin chains are fundamental models in condensed matter physics.
  • Understanding ground states and phase transitions is crucial for materials science.

Purpose of the Study:

  • To investigate the ground states of spin S Heisenberg spin chains with a three-body interaction.
  • To generalize the Majumdar-Ghosh point and analyze phase transitions.

Main Methods:

  • Analytical solution for specific interaction ratios.
  • Density Matrix Renormalization Group (DMRG) for S=1 spin chains.
  • Strong-coupling expansion of the Hubbard model.

Main Results:

  • Fully dimerized ground states are found for spin S chains at a specific three-body interaction ratio: 1/[4S(S+1)-2].
  • This generalizes the Majumdar-Ghosh point for S=1/2.
  • For S=1, a continuous phase transition (central charge c=3/2) between Haldane and dimerized phases was observed.
  • The three-body interaction naturally emerges from the Hubbard model.

Conclusions:

  • The studied three-body interaction drives dimerization in spin chains.
  • The findings provide insights into the behavior of real antiferromagnetic materials.
  • This work extends the understanding of exactly solvable points in quantum magnetism.