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Correlation Inequalities for the Quantum XY Model.

Costanza Benassi1, Benjamin Lees1, Daniel Ueltschi1

  • 1Department of Mathematics, University of Warwick, Coventry, CV4 7AL UK.

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|August 23, 2016
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Summary
This summary is machine-generated.

We proved the sign of truncated correlation functions for quantum XY models. This extends Griffiths-Ginibre inequalities to quantum systems, generalizing prior work.

Keywords:
Correlation inequalitiesGriffiths inequalitiesQuantum XY model

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Area of Science:

  • Statistical Mechanics
  • Quantum Many-Body Physics

Background:

  • The quantum XY model is a fundamental model in condensed matter physics.
  • Correlation functions provide insights into system properties.

Purpose of the Study:

  • To determine the positivity or negativity of truncated correlation functions.
  • To generalize Griffiths-Ginibre inequalities to quantum systems.

Main Methods:

  • Analysis of truncated correlation functions.
  • Application to the quantum XY model with spin 1/2 and spin 1.

Main Results:

  • Established the sign of truncated correlation functions for spin 1/2 at any temperature.
  • Determined the sign for spin 1 in the ground state.
  • Demonstrated the generalization of Griffiths-Ginibre inequalities.

Conclusions:

  • The study provides new inequalities for quantum correlation functions.
  • Results extend classical statistical mechanics findings to the quantum realm.