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Quantum spherical spin models.

R Serral Gracià1, Th M Nieuwenhuizen

  • 1Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands. rubeng@science.uva.nl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
Summary

This study analyzes quantum spherical spin models, revealing how different Hamiltonians impact quantum critical phenomena. The findings offer insights into quantum magnetism and phase transitions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Quantum spherical spin models offer a unique framework for studying quantum magnetism.
  • The inclusion or exclusion of kinetic terms in the Hamiltonian leads to distinct symmetry classes.

Purpose of the Study:

  • To analyze two specific quantum spherical spin models with different Hamiltonian structures.
  • To investigate the impact of these structural differences on phase diagrams and quantum critical phenomena.

Main Methods:

  • Exact solvability of the models was utilized.
  • Phase diagrams were analyzed, focusing on the behavior under a transversal external field.
  • Symmetries of the Hamiltonians were examined to understand critical phenomena.

Main Results:

  • Both models exhibit a phase transition line under a transversal field, culminating in a quantum critical point.
  • Different Hamiltonian symmetries lead to distinct critical phenomena in the quantum critical region.
  • One model mirrors the large-N limit of SU(N) Heisenberg ferromagnets, while the other aligns with SU(N) Heisenberg antiferromagnets.

Conclusions:

  • The inclusion of momenta in the Hamiltonian significantly alters quantum critical behavior.
  • These models provide valuable theoretical tools for understanding diverse quantum magnetic systems and their phase transitions.

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