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Interaction picture density matrix quantum Monte Carlo.

Fionn D Malone1, N S Blunt2, James J Shepherd1

  • 1Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom.

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|August 3, 2015
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Summary
This summary is machine-generated.

The density matrix quantum Monte Carlo (DMQMC) algorithm offers exact properties for quantum systems. Applying it to interacting fermions in the warm dense regime shows significant benefits, with benchmark calculations for a four-electron system.

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Area of Science:

  • Quantum Many-Body Physics
  • Computational Quantum Chemistry

Background:

  • The density matrix quantum Monte Carlo (DMQMC) algorithm enables exact sampling of the N-body thermal density matrix.
  • Accessing exact properties of quantum systems at arbitrary temperatures is crucial for understanding material behavior.

Purpose of the Study:

  • To demonstrate the benefits of using the interaction picture within the DMQMC algorithm for interacting fermions.
  • To investigate and extrapolate basis set incompleteness error at finite temperatures.
  • To perform benchmark calculations for the uniform electron gas in the warm dense regime.

Main Methods:

  • Stochastic sampling of the N-body thermal density matrix using DMQMC.
  • Application of the interaction picture to interacting fermion systems.
  • Monte Carlo sampling for basis set incompleteness error extrapolation.
  • Benchmark calculations for a four-electron system.

Main Results:

  • The interaction picture offers substantial advantages for DMQMC applied to interacting fermions.
  • Basis set incompleteness error at finite temperatures can be investigated and extrapolated.
  • Benchmark results for a four-electron system are provided.

Conclusions:

  • The DMQMC algorithm, particularly with the interaction picture, is a powerful tool for studying interacting fermions.
  • Accurate calculations for systems like the warm dense electron gas are achievable.
  • The methodology provides a foundation for future studies on complex quantum systems.