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Introduction

  • Adam Iaizzi
Chapter
  • 139 Downloads
Part of the Springer Theses book series (Springer Theses)

Abstract

This dissertation describes a study of phase transitions in low-dimensional quantum magnets (specifically the J-Q model) in the presence of external fields using numerical methods, chiefly stochastic series expansion quantum Monte Carlo. In this introduction I have taken special care to describe the historical and scientific context for both the problems studied in this work and the numerical methods used to study them in a manner accessible to the non-expert. I begin with a brief history of computational physics, focusing on the underappreciated role of women in the foundation of the field. I also chronicle the history of the Monte Carlo method, presenting the little-known story of Dr. Arianna Wright Rosenbluth, who wrote the first-ever Metropolis Algorithm Monte Carlo program. From there I describe in broad terms the field of condensed matter physics and the more specific topics covered by this dissertation including phase transitions, quantum phase transitions (including deconfined quantum criticality), and the nature of quasiparticles. Finally, I discuss the larger motivations for the study described in this dissertation.

References

  1. 1.
    A.W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007). https://doi.org/10.1103/PhysRevLett.98.227202 ADSCrossRefGoogle Scholar
  2. 2.
    A.W. Sandvik, in American Institute of Physics Conference Series, vol. 1297, ed. by A. Avella, F. Mancini (2010), pp. 135–338. https://doi.org/http://arxiv.org/abs/1101.3281
  3. 3.
    R.G. Melko, R.K. Kaul, Phys. Rev. Lett. 100, 017203 (2008). https://doi.org/10.1103/PhysRevLett.100.017203 ADSCrossRefGoogle Scholar
  4. 4.
    A.W. Sandvik, Phys. Rev. Lett. 104, 177201 (2010). https://doi.org/10.1103/PhysRevLett.104.177201 ADSCrossRefGoogle Scholar
  5. 5.
    A.W. Sandvik, V.N. Kotov, O.P. Sushkov, Phys. Rev. Lett. 106, 207203 (2011). https://doi.org/10.1103/PhysRevLett.106.207203 ADSCrossRefGoogle Scholar
  6. 6.
    S. Sanyal, A. Banerjee, K. Damle, Phys. Rev. B 84, 235129 (2011). https://doi.org/10.1103/PhysRevB.84.235129 ADSCrossRefGoogle Scholar
  7. 7.
    Y. Tang, A.W. Sandvik, Phys. Rev. Lett. 107, 157201 (2011). https://doi.org/10.1103/PhysRevLett.107.157201 ADSCrossRefGoogle Scholar
  8. 8.
    Y. Tang A.W. Sandvik, Phys. Rev. B 92, 184425 (2015). https://doi.org/10.1103/PhysRevB.92.184425 ADSCrossRefGoogle Scholar
  9. 9.
    H. Suwa, A. Sen, A.W. Sandvik, Phys. Rev. B 94, 144416 (2016). https://doi.org/10.1103/PhysRevB.94.144416 ADSCrossRefGoogle Scholar
  10. 10.
    H. Shao, W. Guo, A.W. Sandvik, Science 352, 213 (2016). https://doi.org/10.1126/science.aad5007 ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    A. Iaizzi, A.W. Sandvik, J. Phys. Conf. Ser. 640, 012043 (2015). http://stacks.iop.org/1742-6596/640/i=1/a=012043 CrossRefGoogle Scholar
  12. 12.
    A. Iaizzi, K. Damle, A.W. Sandvik, Phys. Rev. B 95, 174436 (2017). https://doi.org/10.1103/PhysRevB.95.174436 ADSCrossRefGoogle Scholar
  13. 13.
    S. Sachdev, T. Senthil, R. Shankar, Phys. Rev. B 50, 258 (1994). https://doi.org/10.1103/PhysRevB.50.258 ADSCrossRefGoogle Scholar
  14. 14.
    A. Iaizzi, K. Damle, A.W. Sandvik, Phys. Rev. B 98, 064405 (2018). https://doi.org/10.1103/PhysRevB.98.064405 ADSCrossRefGoogle Scholar
  15. 15.
    T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, M.P.A. Fisher, Science 303, 1490 (2004). https://doi.org/10.1126/science.1091806 ADSCrossRefGoogle Scholar
  16. 16.
    T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, M.P.A. Fisher, Phys. Rev. B 70, 144407 (2004). https://doi.org/10.1103/PhysRevB.70.144407 ADSCrossRefGoogle Scholar
  17. 17.
    J. Lou, A.W. Sandvik, N. Kawashima, Phys. Rev. B 80, 180414 (2009). https://doi.org/10.1103/PhysRevB.80.180414 ADSCrossRefGoogle Scholar
  18. 18.
    S. Jin, A.W. Sandvik, Phys. Rev. B 87, 180404 (2013). https://doi.org/10.1103/PhysRevB.87.180404 ADSCrossRefGoogle Scholar
  19. 19.
    Y. Tang, A.W. Sandvik, Phys. Rev. Lett. 110, 217213 (2013). https://doi.org/10.1103/PhysRevLett.110.217213 ADSCrossRefGoogle Scholar
  20. 20.
    A. Iaizzi, H.D. Scammell, O.P. Sushkov, A.W. Sandvik, Direct numerical observation of Bose-Einstein Condensation of deconfined spinons (2018) (in preparation)Google Scholar
  21. 21.
    S. Brandt, Data Analysis: Statistical and Computational Methods for Scientists and Engineers, 3rd edn. (Springer, Berlin, 1998)zbMATHGoogle Scholar
  22. 22.
    D. Grier, When Computers Were Human (Princeton University Press, Princeton, 2013). https://books.google.com/books?id=YTcDAQAAQBAJ Google Scholar
  23. 23.
  24. 24.
    M. Wolverton, American Heritage 61, 201 (2011). Girl Comput. http://www.americanheritage.com/content/girl-computers Google Scholar
  25. 25.
    J.E. Gubernatis, AIP Conf. Proc. 690, 3 (2003). https://doi.org/10.1063/1.1632111 ADSCrossRefGoogle Scholar
  26. 26.
    N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953). https://doi.org/10.1063/1.1699114 ADSCrossRefGoogle Scholar
  27. 27.
    J.E. Gubernatis, Phys. Plasmas 12, 057303 (2005). https://doi.org/10.1063/1.1887186 ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    K.-H. Barth, Interview of Marshall Rosenbluth, Niels Bohr Library and Archives. Published by American Institute of Physics (2003). https://www.aip.org/history-programs/niels-bohr-library/oral-histories/28636-1
  29. 29.
    M.N. Rosenbluth, AIP Conf. Proc. 690, 22 (2003). https://doi.org/10.1063/1.1632112 ADSCrossRefGoogle Scholar
  30. 30.
  31. 31.
    N. Metropolis, Los Alamos Sci. 15, 125 (1987). Available online at https://library.lanl.gov/cgi-bin/getfile?00326866.pdf Google Scholar
  32. 32.
    R. Ivie, K.N. Ray, AIP Rep. (2005). Women Phys. Astron. https://www.aip.org/statistics/reports/women-physics-and-astronomy-2005
  33. 33.
    Fraction of bachelor’s degrees earned by women, by major . https://www.aps.org/programs/education/statistics/womenmajors.cfm. Credit: American Physical Society, Source: IPEDS Completion Survey. Accessed 3 Nov 2017
  34. 34.
    Doctoral degrees earned by women, by majorhttps://www.aps.org/programs/education/statistics/fraction-phd.cfm, Credit: American Physical Society, Source: IPEDS Completion Survey. Accessed 3 Nov 2017
  35. 35.
    R. Ivie, S. White, R.Y. Chu, Phys. Rev. Phys. Educ. Res. 12, 020109 (2016). https://doi.org/10.1103/PhysRevPhysEducRes.12.020109 CrossRefGoogle Scholar
  36. 36.
    G. Ghiasi, V. Larivière, C.R. Sugimoto, PLoS One 10, 1 (2016). https://doi.org/10.1371/journal.pone.0145931 Google Scholar
  37. 37.
    N. Caplar, S. Tacchella, S. Birrer, Nat. Astron. 1, S41550 (2017). https://doi.org/10.1038/s41550-017-0141 Google Scholar
  38. 38.
    T. Dauxois, Phys. Today 61, 55 (2008). https://doi.org/10.1063/1.2835154 ADSCrossRefGoogle Scholar
  39. 39.
    E. Fermi, P. Pasta, S. Ulam, M. Tsingou, Los Alamos Rep. (1955). https://doi.org/10.2172/4376203. Author’s note: although Tsingou is not listed as an author on the original paper, the preferred citations of the paper has since been amended to include Tsingou. https://www.osti.gov/biblio/4376203-studies-nonlinear-problems
  40. 40.
  41. 41.
    Harvard University Alumni Directory https://alumni.harvard.edu/help/directory-search (2017). Accessed 20 Nov 2017. Not accessible to public
  42. 42.
    Harvard Physics PhD Theses 1873–1953 Harvard Physics Department Website: https://www.physics.harvard.edu/uploads/files/thesesPDF/PhD1873-1953.pdf (2017). Accessed 21 Nov 2017
  43. 43.
  44. 44.
    A. Wright, Some Aspects of Paramagnetic Relaxation. Ph.D. thesis, Radcliffe College (1949). Supervised by J.H. Van Vleck at Harvard UniversityADSCrossRefGoogle Scholar
  45. 45.
  46. 46.
    J. Hodgman, Vacationland: True Stories from Painful Beaches (Penguin Publishing Group, London, 2017). https://books.google.com/books?id=7BgcDgAAQBAJ Google Scholar
  47. 47.
    P.M. Chaikin T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1998)Google Scholar
  48. 48.
    N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966). https://doi.org/10.1103/PhysRevLett.17.1133 ADSCrossRefGoogle Scholar
  49. 49.
  50. 50.
    R.K. Pathria, P.D. Beale, Statistical Mechanics, 3rd edn. (Elsevier, Amsterdam, 2011)zbMATHGoogle Scholar
  51. 51.
    C.K. Majumdar, D.K. Ghosh, J. Math. Phys. 10, 1388 (1969). https://doi.org/10.1063/1.1664978 ADSCrossRefGoogle Scholar
  52. 52.
    C.K. Majumdar, D.K. Ghosh, J. Math. Phys. 10, 1399 (1969). https://doi.org/10.1063/1.1664979 ADSCrossRefGoogle Scholar
  53. 53.
    N. Blanc, J. Trinh, L. Dong, X. Bai, A.A. Aczel, M. Mourigal, L. Balents, T. Siegrist, A.P. Ramirez, Nat. Phys. 14, 273 (2017). https://doi.org/10.1038/s41567-017-0010-y CrossRefGoogle Scholar
  54. 54.
    R.B. Laughlin, Science 303, 1475 (2004). https://doi.org/10.1126/science.1095266 CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of PhysicsNational Taiwan UniversityTaipeiTaiwan

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