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Open Access Publications from the University of California

Quantum magnetism on small-world networks

  • Author(s): Dupont, M;
  • Laflorencie, N
  • et al.

While classical spin systems in random networks have been intensively studied, much less is known about quantum magnets in random graphs. Here, we investigate interacting quantum spins on small-world networks, building on mean-field theory and extensive quantum Monte Carlo simulations. Starting from one-dimensional (1D) rings, we consider two situations: All-to-all interacting and long-range interactions randomly added. The effective infinite dimension of the lattice leads to a magnetic ordering at finite temperature Tc with mean-field criticality. Nevertheless, in contrast to the classical case, we find two distinct power-law behaviors for Tc versus the average strength of the extra couplings. This is controlled by a competition between a characteristic length scale of the random graph and the thermal correlation length of the underlying 1D system, thus challenging mean-field theories. We also investigate the fate of a gapped 1D spin chain against the small-world effect.

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