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Imaginary time density-density correlations for two-dimensional electron gases at high density.

M Motta1, D E Galli1, S Moroni2

  • 1Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy.

The Journal of Chemical Physics
|November 2, 2015
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Summary

The phaseless auxiliary field quantum Monte Carlo method successfully calculates imaginary time correlation functions for homogeneous electron gases. This approach enables the study of dynamical properties in medium-sized fermion systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems

Background:

  • Homogeneous electron gases (HEGs) are fundamental models in condensed matter physics.
  • Accurate calculation of dynamical properties in these systems is computationally challenging.

Purpose of the Study:

  • To evaluate imaginary time density-density correlation functions for 2D HEGs using the phaseless auxiliary field quantum Monte Carlo (AFQMC) method.
  • To assess the capability of phaseless AFQMC for medium-sized fermion systems.
  • To investigate the computational feasibility and limitations of the method.

Main Methods:

  • Phaseless auxiliary field quantum Monte Carlo (AFQMC) method.
  • Periodic boundary conditions and a basis set of up to 300 plane waves.
  • Numerical stabilization techniques for matrix operations (exponentials, products, inversions).
  • Inverse Laplace transform of correlation functions.

Main Results:

  • Demonstrated the feasibility of calculating imaginary time correlation functions for systems up to 42 particles.
  • Identified necessary numerical stabilization techniques for handling large matrices.
  • Quantitatively presented limitations concerning system size.
  • Assessed the method's ability to compute dynamical properties via inverse Laplace transform.

Conclusions:

  • Phaseless AFQMC, with appropriate stabilization, provides access to correlation functions for medium-sized 2D HEGs.
  • The method shows promise for evaluating dynamical properties of homogeneous fermion systems.
  • Understanding computational complexity and system size limitations is crucial for application.