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Constrained sampling method for analytic continuation.

Anders W Sandvik1

  • 1Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA and Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China.

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Summary
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This study introduces a new method for analytic continuation, improving spectral function accuracy by suppressing errors from configurational entropy in quantum Monte Carlo simulations.

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Area of Science:

  • Condensed Matter Physics
  • Computational Physics

Background:

  • Analytic continuation is crucial for deriving real-frequency spectral functions from imaginary-time data.
  • Existing methods often suffer from distortions due to configurational entropy in quantum Monte Carlo simulations.

Purpose of the Study:

  • To develop a novel method for analytic continuation of imaginary-time correlation functions.
  • To overcome limitations of previous methods by addressing configurational entropy.
  • To accurately compute real-frequency spectral functions.

Main Methods:

  • A stochastic sampling approach is employed, parametrizing the spectrum with numerous delta functions.
  • The problem is reframed as a statistical-mechanics problem.
  • Entropy is suppressed by constraining spectral weight and fixing the number of peaks.

Main Results:

  • The method successfully avoids distortions caused by configurational entropy.
  • The dynamic structure factor of the S=1/2 Heisenberg chain was computed.
  • Excellent agreement was achieved with Bethe ansatz and exact diagonalization results.

Conclusions:

  • The proposed method offers a robust way to perform analytic continuation.
  • It provides accurate spectral functions, particularly for systems like the Heisenberg chain.
  • This technique enhances the reliability of quantum Monte Carlo simulation results.