Skip to main content
SpringerLink
Log in

A Survey on Reptation Quantum Monte Carlo

  • Chapter
  • First Online:
Advances in the Theory of Quantum Systems in Chemistry and Physics

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 22))

Abstract

We review the conceptual and mathematical foundations of reptation quantum Monte Carlo and its variants, placing them in the context of other path integral-based methods and the commonly-used diffusion Monte Carlo method. We describe quantum Monte Carlo sampling from the pure distribution, and strategies to improve the efficiency of this sampling. This is followed by a compilation of applications to electronic structure problems and to those in condensed matter physics. We conclude by reflecting on potential improvements of quantum Monte Carlo algorithms and how they will evolve with developments in high performance computing.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ceperley DM (2010) Theoretical and computational methods in mineral physics: geophysical applications. Rev Mineral Geochem 71:129

    Article  Google Scholar 

  2. Anderson JB (1975) J Chem Phys 63:1499

    Article  CAS  Google Scholar 

  3. Ceperley DM, Alder BJ (1980) Phys Rev Lett 45:566

    Article  CAS  Google Scholar 

  4. Hammond BL, Lester WA Jr, Reynolds PJ (1994) Monte Carlo methods and ab initio quantum chemistry. World Scientific, Singapore

    Google Scholar 

  5. Anderson JB, Rothstein SM (eds) (2007) Advances in quantum Monte Carlo. American Chemical Society, Washington, DC

    Google Scholar 

  6. Anderson JB (2007) Quantum Monte Carlo: origins, development, applications. Oxford University Press, Oxford, New York

    Google Scholar 

  7. Huang P, Carter EA (2008) Annu Rev Phys Chem 59:261

    Article  CAS  Google Scholar 

  8. Lester WA Jr, Mitas L, Hammond B (2009) Chem Phys Lett 478:1

    Article  CAS  Google Scholar 

  9. Reynolds PJ, Ceperley DM, Alder BJ, Lester WA Jr (1982) J Chem Phys 77:5593

    Article  CAS  Google Scholar 

  10. Anderson JB (1976) J Chem Phys 65:4121

    Article  CAS  Google Scholar 

  11. Reynolds PJ, Barnett RN, Hammond BL, Lester WA Jr (1986) J Stat Phys 43:1017

    Article  Google Scholar 

  12. Barnett RN, Reynolds PJ, Lester WA Jr (1992) J Chem Phys 96:2141

    Article  CAS  Google Scholar 

  13. Langfelder P, Rothstein SM, Vrbik J (1997) J Chem Phys 107:8525

    Article  CAS  Google Scholar 

  14. Hornik M, Rothstein SM (2002) In: Lester WA Jr, Rothstein SM, Tanaka S (eds) Recent advances in quantum Monte Carlo methods; Part II. World Scientific, Singapore, pp 71–94

    Chapter  Google Scholar 

  15. Baroni S, Moroni S (1999) Phys Rev Lett 82:4745

    Article  CAS  Google Scholar 

  16. Baroni S, Moroni S (1999) In: Nightingale MP, Umrigar CJ (eds) Quantum Monte Carlo methods in physics and chemistry. Kluwer, Dordrecht

    Google Scholar 

  17. Umrigar CJ, Nightingale MP, Runge KJ (1993) J Chem Phys 99:2865

    Article  CAS  Google Scholar 

  18. Grossman JC (2002) J Chem Phys 117:1434

    Article  CAS  Google Scholar 

  19. Bosá I, Rothstein SM (2004) J Chem Phys 121:4486

    Article  Google Scholar 

  20. Yuen WK, Farrar T, Rothstein SM (2007) J Phys A 40:F639

    Article  CAS  Google Scholar 

  21. Coles B, Vrbik P, Giacometti RD, Rothstein SM (2008) J Phys Chem A 112:2012

    Article  CAS  Google Scholar 

  22. Yuen WK, Oblinsky DG, Giacometti RD, Rothstein SM (2009) Intern J Quantum Chem 109:3229

    Article  CAS  Google Scholar 

  23. Yuen WK, Oblinsky DG, Rothstein SM (2009) (unpublished)

    Google Scholar 

  24. Oblinsky DG, Yuen WK, Rothstein SM (2010) J Molec Struct Theochem 961:29

    Article  CAS  Google Scholar 

  25. Metropolis N, Rosenbluth AW, Teller AH, Teller E (1953) J Chem Phys 21:1087

    Article  CAS  Google Scholar 

  26. Hastings WK (1970) Biometrica 57:97

    Article  Google Scholar 

  27. Ceperley DM (1995) Rev Mod Phys 67:279

    Article  CAS  Google Scholar 

  28. Pierleoni C, Ceperley DM (2005) ChemPhysChem 6:1872

    Article  CAS  Google Scholar 

  29. Carleo G, Becca F, Moroni S, Baroni S (2010) Phys Rev E 82:046710

    Article  Google Scholar 

  30. Cuervo JE, Roy P-N, Boninsegni M (2005) J Chem Phys 122:114504

    Article  Google Scholar 

  31. Ceperely DM, Chester GV, Kalos MH (1977) Phys Rev B 16:3081

    Article  Google Scholar 

  32. Tierney L (1994) Ann Stat 22:1701

    Article  Google Scholar 

  33. Roberts GO, Rosenthal JS (2001) Stat Sci 16:351

    Article  Google Scholar 

  34. Wagner LK, Mitas L (2007) J Chem Phys 126:034105

    Article  Google Scholar 

  35. Wagner LK (2007) J Phys Condens Matter 19:343201

    Article  Google Scholar 

  36. Wu X, Hu X, Dai Y, Du C, Chu S, Hu L, Deng J, Feng Y (2010) J Chem Phys 132:204304

    Article  Google Scholar 

  37. Kanai Y, Grossman JC (2009) Phys Rev A 80:032504

    Article  Google Scholar 

  38. Dewing M, Ceperley DM (2002) In: Lester WA Jr, Rothstein SM, Tanaka S (eds) Recent advances in quantum Monte Carlo II. World Scientific, River Edge

    Google Scholar 

  39. Ceperley DM, Dewing M, Pierleoni C (2002) Lect Notes Phys 605:473

    Article  Google Scholar 

  40. Pierleoni C, Ceperley DM (2006) Lect Notes Phys 703:641

    Article  CAS  Google Scholar 

  41. Morales MA, Pierleoni C, Ceperley DM (2010) Phys Rev E 81:021202

    Article  Google Scholar 

  42. Moroni S, Sarsa A, Fantoni S, Schmidt KE, Baroni S (2003) Phys Rev Lett 90:143401

    Article  Google Scholar 

  43. Cazzato P, Paolini S, Moroni S, Baroni S (2004) J Chem Phys 120:9071

    Article  CAS  Google Scholar 

  44. Tang J, McKellar ARW, Mezzacapo F, Moroni S (2004) Phys Rev Lett 92:145503

    Article  CAS  Google Scholar 

  45. Moroni S, Blinov N, Roy P-N (2004) J Chem Phys 121:3577

    Article  CAS  Google Scholar 

  46. Moroni S, Botti M, DePalo S, McKellar ARW (2005) J Chem Phys 122:094314

    Article  CAS  Google Scholar 

  47. Baroni S, Moroni S (2005) ChemPhysChem 6:1884

    Article  CAS  Google Scholar 

  48. Topic W, Jäger W, Blinov N, Roy P-N, Botti M, Moroni S (2006) J Chem Phys 125:144310

    Article  CAS  Google Scholar 

  49. Škrbić T, Moroni S, Baroni S (2007) J Phys Chem A 111:7640

    Article  Google Scholar 

  50. Škrbić T, Moroni S, Baroni S (2007) J Phys Chem A 111:12749

    Article  Google Scholar 

  51. Gori-Giorgi P, Moroni S, Bachelet GB (2004) Phys Rev B 70:115102

    Article  Google Scholar 

  52. Citro R, Orignac E, De Palo S, Chiofalo ML (2007) Phys Rev A 75:051602

    Article  Google Scholar 

  53. Citro R, De Palo S, Orignac E, Pedri P, Chiofalo ML (2008) New J Phys 10:045011

    Article  Google Scholar 

  54. Pedri P, De Palo S, Orignac E, Citro R, Chiofalo ML (2008) Phys Rev A 77:015601

    Article  Google Scholar 

  55. De Palo S, Orignac E, Citro R, Chiofalo ML (2008) Phys Rev B 77:212101

    Article  Google Scholar 

  56. Syljuåsen OF (2005) Phys Rev B 71:020401 (R)

    Google Scholar 

  57. Syljuåsen OF (2006) Phys Rev B 73:245105

    Article  Google Scholar 

  58. Anderson JB (1987) Phys Rev A 35:3550

    Article  CAS  Google Scholar 

  59. Ceperley DM (1991) J Stat Phys 63:1237

    Article  Google Scholar 

  60. Glauser WA, Brown WR, Lester WA Jr, Bressanini D, Hammond BL, Koszykowski ML (1992) J Chem Phys 97:9200

    Article  CAS  Google Scholar 

  61. Bressanini D, Ceperely DM, Reynolds PJ (2002) In: Lester WA Jr, Rothstein SM, Tanaka S (eds) Recent advances in quantum Monte Carlo II. World Scientific, Edge, pp 3–11

    Chapter  Google Scholar 

  62. Foulkes WMC, Hood RQ, Needs RJ (1999) Phys Rev B 60:4558

    Article  CAS  Google Scholar 

  63. Mitas L (2006) Phys Rev Lett 96:240402

    Article  Google Scholar 

  64. Bajdick M, Mitas L, Wagner LK, Schmidt KE (2008) Phys Rev B 77:115112

    Article  Google Scholar 

  65. Kruger F, Zaanen J (2008) Phys Rev B 78:035104

    Article  Google Scholar 

  66. Bressanini D, Morosi G (2008) J Chem Phys 129:054103

    Article  Google Scholar 

  67. Bouabça T, Braïda B, Caffarel M (2010) J Chem Phys 133:044111

    Article  Google Scholar 

  68. Booth GH, Thom AJW, Alavi A (2009) J Chem Phys 131:054106

    Article  Google Scholar 

  69. Booth GH, Alavi A (2010) J Chem Phys 132:174104

    Article  Google Scholar 

  70. Kim J, Esler K, McMinis J, Clark B, Gergely J, Chiesa S, Delaney K, Vincent J, Ceperley DM. QMCPACK simulation suite. http://qmcpack.cmscc.org

  71. Kim J, Esler KP, McMinis J, Ceperley DM (2010) SciDAC Proceedings

    Google Scholar 

Download references

Acknowledgements

This work was supported, in part, by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC).

Author information

Authors and Affiliations

  1. Department of Mathematics, Brock University, St. Catharines, Ontario, Canada, L2S 3A1

    Wai Kong Yuen

  2. Departments of Chemistry and Physics, Brock University, St. Catharines, Ontario, Canada, L2S 3A1

    Stuart M. Rothstein

Authors
  1. Wai Kong Yuen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stuart M. Rothstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. , LASMEA, Clermont University, avenue des Landais 24, Aubiere Cedex, 63177, France

    Philip E. Hoggan

  2. Dept. Quantum Chemistry, Uppsala University, Uppsala, Sweden

    Erkki J. Brändas

  3. Labo. Chimie Physique, CNRS, rue Pierre et Marie Curie 11, Paris, 75005, France

    Jean Maruani

  4. Dept. Chemistry, Michigan State University, Chemistry Building, East Lansing, 48824, Michigan, USA

    Piotr Piecuch

  5. Inst. Matemáticas y Física, Fundamental (IMAFF), CSIC Madrid, C/ Serrano 123, Madrid, 28006, Spain

    Gerardo Delgado-Barrio

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Yuen, W.K., Rothstein, S.M. (2012). A Survey on Reptation Quantum Monte Carlo. In: Hoggan, P., Brändas, E., Maruani, J., Piecuch, P., Delgado-Barrio, G. (eds) Advances in the Theory of Quantum Systems in Chemistry and Physics. Progress in Theoretical Chemistry and Physics, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2076-3_18

Download citation

Publish with us

Policies and ethics

Search

Navigation