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Classical height models with topological order.

Christopher L Henley1

  • 1Department of Physics, Cornell University, Ithaca, NY 14853-2501, USA.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|April 8, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces statistical-mechanics models on lattices with finite group elements, focusing on topological order and non-Abelian properties. It provides criteria for model viability and Monte Carlo updates.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Group theory

Background:

  • Lattice models are fundamental in statistical mechanics.
  • Topological order describes phases of matter robust to local perturbations.
  • Finite group theory provides a framework for discrete symmetries.

Purpose of the Study:

  • To explore statistical-mechanics models on lattices with finite group elements.
  • To investigate the emergence and properties of topological order, including non-Abelian topological order.
  • To establish criteria for the viability and simulation of these models.

Main Methods:

  • Construction of statistical-mechanics models on directed lattices.
  • Application of group theory constraints (plaquette product equals identity).
  • Analysis of topological order and symmetry-related thermodynamic components.
  • Development of criteria for model viability and Monte Carlo updates.

Main Results:

  • A family of statistical-mechanics models is presented where lattice edges are occupied by elements of a finite group G.
  • The constraint that the product around any plaquette must be the group identity (e) is imposed.
  • The potential for these models to exhibit topological order, including non-Abelian topological order when G is non-Abelian, is demonstrated.
  • Criteria for assessing the viability of specific models and their suitability for Monte Carlo simulations are derived.

Conclusions:

  • The discussed models offer a framework for studying topological order in systems with finite group symmetries.
  • Non-Abelian groups can lead to non-Abelian topological order, a key feature for topological quantum computing.
  • The provided criteria are essential for the practical implementation and study of these novel statistical-mechanics models.