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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Published on: May 27, 2020

Extrapolated high-order propagators for path integral Monte Carlo simulations.

Robert E Zillich¹, Johannes M Mayrhofer, Siu A Chin

¹Institut für Theoretische Physik, Johannes Kepler Universität Linz, A-4040 Linz, Austria. robert.zillich@jku.at

The Journal of Chemical Physics

|February 2, 2010

Summary

This summary is machine-generated.

We developed novel high-order imaginary time propagators for path integral Monte Carlo simulations. These new algorithms improve accuracy without needing complex calculations, enabling more efficient quantum many-body system studies.

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Area of Science:

Computational Physics
Quantum Many-Body Systems

Background:

Path integral Monte Carlo (PIMC) simulations are crucial for studying quantum many-body systems.
Higher-order propagators in PIMC can improve accuracy but often require computationally expensive terms like high-order derivatives or explicit Gaussian quadratures.

Purpose of the Study:

To introduce a new class of high-order imaginary time propagators for PIMC simulations.
To develop algorithms that avoid the need for higher-order potential derivatives and explicit Gaussian trajectory quadratures.
To demonstrate the feasibility of achieving arbitrarily high-order convergence in PIMC.

Main Methods:

Extrapolation of the primitive second-order propagator using subtractions to achieve higher orders.
Ensuring all terms in the extrapolated propagator share the same Gaussian trajectory, localizing the subtraction to the potential term.
Verifying algorithm convergence by calculating the ground state energy and pair distribution function of liquid Helium-4.

Main Results:

The new propagators achieve high-order convergence (fourth, sixth, and eighth order verified).
Despite a theoretical violation of positivity, the algorithms maintain accuracy at practical time steps.
The method successfully simulates a dense, strongly interacting quantum system (liquid 4He).

Conclusions:

A novel, efficient class of high-order imaginary time propagators for PIMC has been developed.
These algorithms offer a practical route to arbitrarily high-order accuracy in PIMC simulations.
The method is validated for strongly correlated quantum systems like liquid Helium-4.