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Systematic derivation of order parameters through reduced density matrices.

Shunsuke Furukawa1, Grégoire Misguich, Masaki Oshikawa

  • 1Department of Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan.

Physical Review Letters
|February 21, 2006
PubMed
Summary

A new method uses reduced density matrices to find order parameters in quantum many-body systems. This approach directly reveals exotic orders in ground states without prior knowledge, aiding in the exploration of novel quantum phases.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Many-body systems

Background:

  • Characterizing quantum phases relies on identifying order parameters.
  • Extracting order parameters from complex quantum many-body systems is challenging.
  • Existing methods often require empirical knowledge or are limited in scope.

Purpose of the Study:

  • To develop a systematic and general method for determining order parameters.
  • To enable direct extraction of order parameters from wave functions.
  • To explore unknown and exotic quantum orders.

Main Methods:

  • Utilizing reduced density matrices (RDMs) derived from wave functions.
  • Analyzing degenerate ground states of quantum many-body systems.
  • Applying the method to models with known and potential exotic orders.

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Main Results:

  • A systematic procedure for order parameter determination is established.
  • The method successfully extracts order parameters directly from ground state wave functions.
  • Applicability demonstrated in models exhibiting dimer, scalar chiral, and topological orders.

Conclusions:

  • The developed method provides a powerful tool for characterizing quantum phases.
  • It facilitates the discovery of novel quantum orders without empirical input.
  • This approach opens new avenues for exploring complex quantum phenomena.