Stochastic sampling of quadrature grids for the evaluation of vibrational expectation values

Pablo López Ríos, Bartomeu Monserrat, and Richard J. Needs
Phys. Rev. B 97, 054104 – Published 12 February 2018

Abstract

The thermal lines method for the evaluation of vibrational expectation values of electronic observables [B. Monserrat, Phys. Rev. B 93, 014302 (2016)] was recently proposed as a physically motivated approximation offering balance between the accuracy of direct Monte Carlo integration and the low computational cost of using local quadratic approximations. In this paper we reformulate thermal lines as a stochastic implementation of quadrature-grid integration, analyze the analytical form of its bias, and extend the method to multiple-point quadrature grids applicable to any factorizable harmonic or anharmonic nuclear wave function. The bias incurred by thermal lines is found to depend on the local form of the expectation value, and we demonstrate that the use of finer quadrature grids along selected modes can eliminate this bias, while still offering an 30% lower computational cost than direct Monte Carlo integration in our tests.

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  • Received 16 November 2017

DOI:https://doi.org/10.1103/PhysRevB.97.054104

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Pablo López Ríos1,2,*, Bartomeu Monserrat2,3, and Richard J. Needs2

  • 1Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
  • 2Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
  • 3Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA

  • *pl275@cam.ac.uk

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Issue

Vol. 97, Iss. 5 — 1 February 2018

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