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Related Experiment Videos

Griffiths-McCoy singularities in random quantum spin chains: exact results through renormalization.

F Iglói1, R Juhász, P Lajkó

  • 1Research Institute for Solid State Physics and Optics, H-1525 Budapest, PO Box 49, Hungary.

Physical Review Letters
|February 15, 2001
PubMed
Summary

This study uses the Ma-Dasgupta-Hu renormalization group (RG) scheme to analyze random quantum spin chains. The RG method is shown to be asymptotically exact for critical and Griffiths phases, validated by numerical calculations.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Many-Body Systems

Background:

  • The Griffiths phase in disordered quantum systems exhibits unique singular behavior.
  • Renormalization group (RG) methods are crucial for understanding critical phenomena and phase transitions.
  • Previous analytical solutions for random quantum spin chains were limited in scope.

Purpose of the Study:

  • To apply the Ma-Dasgupta-Hu renormalization group (RG) scheme to study singular quantities in the Griffiths phase of random quantum spin chains.
  • To extend existing analytical solutions to off-critical regions and calculate the dynamical exponent exactly.
  • To investigate the general applicability and asymptotic exactness of the RG method in various random quantum models.

Main Methods:

Related Experiment Videos

  • Utilized the Ma-Dasgupta-Hu renormalization group (RG) scheme.
  • Extended Fisher's analytical solution for the random transverse-field Ising spin chain.
  • Employed scaling considerations to predict the RG method's asymptotic exactness.
  • Performed numerical calculations using the density matrix renormalization group (DMRG) method.

    • Main Results:

    • Successfully extended Fisher's analytical solution to the off-critical region for the random transverse-field Ising spin chain.
    • Calculated the dynamical exponent exactly for this model.
    • Argued and numerically verified that the RG method becomes asymptotically exact for large times in both critical and Griffiths phases for various random quantum chains.
    • Density matrix renormalization group (DMRG) calculations confirmed the RG predictions for random Heisenberg and quantum Potts models.

    Conclusions:

    • The Ma-Dasgupta-Hu RG scheme provides a powerful framework for analyzing disordered quantum systems.
    • The RG method demonstrates asymptotic exactness in critical and Griffiths phases of random quantum spin chains.
    • Numerical validation supports the theoretical predictions, enhancing confidence in the RG approach for complex quantum models.