Coupled Cluster Wave Functions for Ground State Wave Function for Many Physical System

Authors

  • Shashi Bhushan Pandey Research Scholar, University Department of Electronic Science, B.R.A. Bihar University, Muzaffarpur, Bihar 842001, India

DOI:

https://doi.org/10.48165/

Keywords:

Coupled, Cluster, Monte Carlo Algorithm, Configuration Interaction, Hamiltonian, Random Walk, Hilbert Space, Excitations

Abstract

We have studied and found coupled cluster wave functions as important functions  for a projection quantum Monte Carlo algorithm within the configuration interaction  scheme. The ground state wave function of a configuration interaction Hamiltonian  is filtered out by propagating the amplitudes of an initial arbitrary wave function via  a random walk in the many body Hilbert space spanned by a basis of Slater  determinants. The coupled cluster wave functions are used to guide this random  walk via importance sampling in order to circumvent the sign problem. This  approach has provided upper bounds to the ground state energy whose tightness  can be systematically improved by including higher order excitations in the coupled  cluster wave function. We have applied three dimensional homogenous electron gas  in momentum space. The electron gas was studied for large single particle basis  sizes. We found that coupled cluster wave functions are very accurate and good  approximation for ground state wave function for many physical systems. The  obtained results were in good agreement with previously obtained results.

References

. Koldrubet Z. M. and Clark. B. K., (2012), Phys. Rev. B, 86, 075109.

. Both. G. H., Thom. A. J. W. and Alavi A., (2009), J. Chem. Phys. 131, 054106. [3]. Cleland. D, Both. G. H, and Aalvi. A., (2010), J. Chem. Phys. 132, 041103. [4]. Booth. G. H., Gruneis. A, Kresse. G and Alavi. A, (2013), Nature (London), 493, 365. [5]. Kolck. U. Van (1999), Prog. Part, Nucl. Phys. 43, 337.

. Pickett. W. E., (1989), Comput. Phys. Rep. 9, 115.

. Nightingale, M. P. and Umrigarleds. C. J. (1998), Quantum Monte Carlo Methods in Physics and Chemistry (Springer, Berlin, 1998) Vol 525.

. Ceperly. D. M and Mitas. L., (1995), In New Methods in Computational Quantum Mechanics: Advances in Chemical Physics, XC III edited by Prigonine. I. and Rice, S. A., (Wiley. N.Y. 1995) pp -1-38.

. Anderson. J. B., (2007), Rev. Comp. Chem - 13, 133.

. Binder. K. (1995), In the Monte Carlo Method in Condensed Matter, edited by K. Binder, Topics in Applied Physics, Vol-71, (Springer, Heidlberg, 1995).

. Foulkes W.M.C., Mitas L., Needs R.J., and Rajagopal. G., (2001), Rev. Mod. Phys. 73, 33. [12]. Pieper. S.C., (2005), Nucl. Phys. A. 751, 516.

. Reynolds. P. J., Ceperley. D. M., Alder. B.J. and Lester. W. A., Jr, (1982), J. Chem. Phys. 77, 5593.

Downloads

Published

2020-07-01

Issue

Vol. 39 No. 1 (2020): Bulletin of Pure and Applied Sciences Physics (Jan-Jul) 2020

Section

Articles

How to Cite

Coupled Cluster Wave Functions for Ground State Wave Function for Many Physical System . (2020). Bulletin of Pure and Applied Sciences – Physics, 39(1), 117–119. https://doi.org/10.48165/