Skip to main content
SpringerLink
Log in

An overview of coupled cluster theory and its applications in physics

  • Published:
Theoretica chimica acta Aims and scope Submit manuscript

Summary

What has since become known as the normal coupled cluster method (NCCM) was invented about thirty years ago to calculate ground-state energies of closed-shell atomic nuclei. Coupled cluster (CC) techniques have since been developed to calculate excited states, energies of open-shell systems, density matrices and hence other properties, sum rules, and the sub-sum-rules that follow from imbedding linear response theory within the NCCM. Further extensions deal both with systems at nonzero temperature and with general dynamical behaviour. More recently, a new version of CC theory, the so-called extended coupled cluster method (ECCM) has been introduced. It has the potential to describe such global phenomena as phase transitions, spontaneous symmetry breaking, states of topological excitation, and nonequilibrium behaviour. CC techniques are now widely recognized as providing one of the most universally applicable, most powerful, and most accurate of all microscopicab initio methods in quantum many-body theory. The number of successful applications within physics is now impressively large. In most such cases the numerical results are either the best or among the best available. A typical case is the electron gas, where the CC results for the correlation energy agree over the entire metallic density range to within less than 1 millihartree (or <1%) with the essentially exact Green's function Monte Carlo results. The role of CC theory within modern quantum many-body theory is first surveyed, by a comparison with other techniques. Its full range of applications in physics is then reviewed. These include problems in nuclear physics, both for finite nuclei and infinite nuclear matter; the electron gas; various integrable and nonintegrable models; various relativistic quantum field theories; and quantum spin chain and lattice models. Particular applications of the ECCM include the quantum hydrodynamics of a zero-temperature, strongly-interacting condensed Bose fluid; a charged impurity in a polarizable medium (e.g., positron annihilation in metals); and various anharmonic oscillator and spin systems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Mukherjee D (ed) (1989) Aspects of many-body effects in molecules and extended systems. (Lect Notes Chem, vol 50) Springer, Berlin Heidelberg New York

    Google Scholar 

  2. Bartlett RJ (1989) J Phys Chem 93:1697

    Google Scholar 

  3. Coester F (1958) Nucl Phys 7:421

    Google Scholar 

  4. Coester F, Kümmel H (1960) Nucl Phys 17:477

    Google Scholar 

  5. Čižek J (1966) J Chem Phys 45:4256; idem (1969) Advan Chem Phys 14:35

    Google Scholar 

  6. Paldus, J, Čižek J, Shavitt I (1972) Phys Rev A 5:50

    Google Scholar 

  7. Noga J, Bartlett RJ (1987) J Chem Phys 86:7041; idem (1988) ibid 89:3401(E)

    Google Scholar 

  8. Scuseria GE, Schaefer HF (1988) Chem Phys Lett 146:23; idem (1988) ibid 152:382

    Google Scholar 

  9. Bartlett RJ, Purvis GD (1978) Int J Quantum Chem 14:561; idem (1980) Phys Scr 21:251

    Google Scholar 

  10. Pople JA, Krishnan R, Schlegel HB, Binkley JS (1978) Int J Quantum Chem 14:545

    Google Scholar 

  11. Purvis GD, Bartlett RJ (1982) J Chem Phys 76:1910

    Google Scholar 

  12. Bartlett RJ (1981) Annu Rev Phys Chem 32:359

    Google Scholar 

  13. Bishop RF, Kümmel HG (1987) Phys Today 40(3):52

    Google Scholar 

  14. Binder K (ed) (1979) Monte Carlo methods in statistical physics. Springer, New York

    Google Scholar 

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

    Google Scholar 

  16. Kalos MH, Whitlock PA (1986) Monte Carlo methods. Wiley, New York

    Google Scholar 

  17. Guardiola R (1988) Monte Carlo techniques in the many-body problem. In: Prosperi D, Rosati S, Violini G (eds) First international course on condensed matter. (ACIF Series, vol. 8) World Scientific, Singapore, p 157

    Google Scholar 

  18. Day BD (1978) Rev Mod Phys 50:495; idem (1979) Nucl Phys A328:1

    Google Scholar 

  19. Mahaux C (1979) Nucl Phys A328:24

    Google Scholar 

  20. Day BD (1981) in: Molinari A (ed) From nuclei to particles. North-Holland, Amsterdam

    Google Scholar 

  21. Bohm D, Pines D (1951) Phys Rev 82:625; idem (1953) ibid 92:609; Pines D (1953) ibid 92:626

    Google Scholar 

  22. Gell-Mann M, Brueckner KA (1957) Phys Rev 106:364

    Google Scholar 

  23. Kümmel H, Lührmann KH, Zabolitzky JG (1978) Phys Rep 36C:1

    Google Scholar 

  24. Kümmel HG (1984) The coupled cluster method. In: Wu SS, Kuo TTS (eds) Nucleon-nucleon interaction and nuclear many-body problems. World Scientific, Singapore, p 46

    Google Scholar 

  25. Kvasnička V, Laurinc V, Biskupič S (1979) Chem Phys Lett 73:81; Guest MF, Wilson S (1980) ibid 73:607; Frisch MJ, Krishnan R, Pople JA (1980) ibid 75:66; Bartlett RJ, Sekino H, Purvis GD (1983) ibid 98:66

    Google Scholar 

  26. Linderberg J, Öhrn Y (1973) Propagators in quantum chemistry. Academic, London

    Google Scholar 

  27. Öhrn Y (1989) Propagators for molecular electronic spectra. In: Mukherjee D (ed) Aspects of many-body effects in molecules and extended systems. (Lect Notes Chem, vol 50) Springer, Berlin Heidelberg New York, p 187; Oddershede J, Sengeløv PW (1989) Transition moments in RPA-like approximations. In: ibid, p 207

    Google Scholar 

  28. Diatlov IT, Sudakhov VV, Ter-Matirosian KA (1957) Sov Phys — JETP 5:631

    Google Scholar 

  29. Roulet R, Gavoret J, Nozières P (1969) Phys Rev 178:1072

    Google Scholar 

  30. Ripka G (1979) Phys Rep 56:1

    Google Scholar 

  31. Jackson AD, Lande A, Smith RA (1982) Phys Rep 86:55

    Google Scholar 

  32. Jackson AD, Lande A, Smith RA (1985) Phys Rev Lett 54:1469; Krotscheck E, Smith RA, Jackson AD (1986) Phys Rev A 33:3535

    PubMed  Google Scholar 

  33. Lande A, Smith RA (1983) Phys Lett 131B:253

    Google Scholar 

  34. Smith RA, Jackson AD (1988) Fermion parquet: the approximations. In: Kallio AJ, Pajanne E, Bishop RF (eds) Recent progress in many-body theories, vol 1. Plenum, New York, p 327; Lande A, Smith RA (1988) Fermion parquet equations. In: ibid, p 335

    Google Scholar 

  35. Smith RA, Lande A (1988) Parquet theory: the diagrams. In: Arponen JS, Bishop RF, Manninen M (eds) Condensed matter theories, vol 3. Plenum, New York, p 1

    Google Scholar 

  36. Jackson AD, Lande, A, Guitink RW, Smith RA (1985) Phys Rev B 31:403

    Google Scholar 

  37. Baym G, Kadanoff LP (1961) Phys Rev 124:287; Baym G (1962) ibid 127:1391

    Google Scholar 

  38. Smith RA (1989) Baym-Kadanoff theory made planar. In: Keller J (ed) Condensed matter theories, vol 4. Plenum, New York, p 129

    Google Scholar 

  39. Jastrow R (1955) Phys Rev 98:1479

    Google Scholar 

  40. Iwamoto F, Yamada M (1957) Prog Theor Phys 17:543

    Google Scholar 

  41. Clark JW, Westhaus P (1968) J Math Phys 9:131; Westhaus P, Clark JW (1968) ibid 9:149

    Google Scholar 

  42. Gaudin M, Gillespie J, Ripka G (1971) Nucl Phys A176:237; Fantoni S, Rosati S (1974) Nuovo Cim 20A:179

    Google Scholar 

  43. Ripka G (1979) Nucl Phys A314:115

    Google Scholar 

  44. Feenberg E (1969) Theory of quantum fluids. Academic, New York

    Google Scholar 

  45. Fantoni S, Rosati S (1974) Lett Nuovo Cim 10:545; idem (1975) Nuovo Cim 25A:593

    Google Scholar 

  46. Krotscheck E, Ristig ML (1974) Phys Lett 48A:17; idem (1975) Nucl Phys A242:389

    Google Scholar 

  47. Clark JW (1979) in: Wilkinson DH (ed) Progress in particle and nuclear physics, vol 2. Pergamon, Oxford, p 89

    Google Scholar 

  48. Pandharipande VR, Wiringa RB (1979) Rev Mod Phys 51:821; Wiringa RB, Pandharipande VR (1979) Nucl Phys A317:1; Owen JC (1979) Phys Lett 82B:23; Lantto LJ, Siemens PJ (1979) Nucl Phys A317:55; Zabolitzky JG (1980) in: Negele JW, Vogt E (eds) Advances in nuclear physics, vol 12. Plenum, New York; Fantoni S, Pandharipande VR (1984) Nucl Phys A427:473

    Google Scholar 

  49. Rosati S, Fantoni S (1981) Correlations in infinite systems. In: Guardiola R, Ros J (eds) The many-body problem, Jastrow correlations versus Brueckner theory. (Lect Notes Phys, vol 138) Springer, Berlin Heidelberg New York, p 1

    Google Scholar 

  50. Rosati S, Viviani M (1988) in: Prosperi D, Rosati S, Violini G (eds) First international course on condensed matter. (ACIF Series, vol 8) World Scientific, Singapore, p 231

    Google Scholar 

  51. Ciofi degli Atti C (1986) Variational methods in the few-body problem. In: Bracci L et al (eds) Perspectives on theoretical nuclear physics. (Proc of the primo convegno su problemi di fisica nucleare teorica, Cortona, Italy, 1985) ETS editrice, Pisa, p 1

    Google Scholar 

  52. Clark JW (1979) Nucl Phys A328:587

    Google Scholar 

  53. Clark JW, Feenberg E (1959) Phys Rev 113:388; Jackson HW, Feenberg E (1961) Ann Phys (NY) 15:266; Feenberg E, Woo CW (1965) Phys Rev 137:A391; Clark JW, Westhaus P (1966) Phys Rev 141:833; idem (1966) ibid 149:990

    Google Scholar 

  54. Clark JW, Mead LR, Krotscheck E, Kürten KE, Ristig ML (1979) Nucl Phys A328:45

    Google Scholar 

  55. Krotscheck E, Clark JW (1979) Nucl Phys A328:73

    Google Scholar 

  56. Clark JW (1981) The correlated wave function approach to finite nuclear systems. In: Guardiola R, Ros J (eds) The many-body problem, Jastrow correlations versus Brueckner theory. (Lect Notes Phys, vol 138) Springer, Berlin Heidelberg New York, p 184

    Google Scholar 

  57. Chen JMC, Clark JW, Sandler DG (1982) Z Phys A305:223, 367

    Google Scholar 

  58. Krotscheck E, Smith RA, Clark JW, Panoff RM (1981) Phys Rev B 24:6383; Flynn MF, Clark JW, Krotscheck E, Smith RA, Panoff RM (1985) ibid 32:2945

    Google Scholar 

  59. Krotscheck E, Clark JW, Jackson AD (1983) Phys Rev B 28:5088

    Google Scholar 

  60. Clark JW, Krotscheck E, Schwesinger B (1984) Phys Lett 143B:287; idem (1985) Anales Fisica A81:116

    Google Scholar 

  61. Bishop RF (1988) Correlated basis functions and all that. In: Kallio AJ, Pajanne E, Bishop RF (eds) Recent progress in many-body theories, vol 1. Plenum, New York, p 385

    Google Scholar 

  62. Clark JW, Ristig ML (1973) Phys Rev C 7:1792; Ristig ML, Clark JW (1973) Nucl Phys A199:351

    Google Scholar 

  63. Mead LR, Clark JW (1980) Phys Lett 90B:331

    Google Scholar 

  64. Krotscheck E, Kümmel H, Zabolitzky JG (1980) Phys Rev A 22:1243; Krotscheck E, Clark JW (1981) Brueckner theory with Jastrow wave functions. In: Guardiola R, Ros J (eds) The many-body problem, Jastrow correlations versus Brueckner theory. (Lect Notes Phys vol 138) Springer, Berlin Heidelberg New York, p 356

    Google Scholar 

  65. Nesbet RK (1958) Phys Rev 109:1632

    Google Scholar 

  66. Cauchy A (1821) Cours d'analyse de l'ecole polytechnique, ouvres complètes vols 2, 3; Macdonald JKL (1933) Phys Rev 43:830

  67. Primas H (1965) in: Sinanoglu O (ed) Modern quantum chemistry, vol II. Academic, New York, p 45

    Google Scholar 

  68. Brueckner KA (1955) Phys Rev 97:1353; idem (1955) ibid 100:36

    Google Scholar 

  69. Lam PM, Clark JW, Ristig ML (1977) Phys Rev B 16:222; Clark JW, Lam PM, Zabolitzky JG, Ristig ML (1978) ibid 17:1147; Ristig ML, Kürten KE, Clark JW (1979) ibid 19:3539; Flynn MF, Clark JW, Panoff RM, Bohigas O, Stringari S (1984) Nucl Phys A427:253

    Google Scholar 

  70. Chen JMC, Clark JW, Krotscheck E, Smith RA (1986) Nucl Phys A451:509

    Google Scholar 

  71. Clark JW, Krotscheck E (1984) in: Kümmel H, Ristig ML (eds) Recent progress in many-body theories. (Lect Notes Phys, vol 198) Springer, Berlin Heidelberg New York, p 127

    Google Scholar 

  72. Fantoni S, Wang X, Tosatti E, Lu Yu (1988) Physica C 153–155:1255; Wang XQ, Fantoni S, Tosatti E, Lu Yu (1990) Correlated spin-density-wave theory. In: Aguilera-Navarro VC (ed) Condensed matter theories, vol 5. Plenum, New York; Ristig ML (1990) Z Phys B 79:351

    Google Scholar 

  73. Dabringhaus A, Ristig ML (1989) TheU(1) lattice gauge model: a correlated many-body system. In: Keller J (ed) Condensed matter theories, vol 4. Plenum, New York; idem (1991) TheU(1)3 lattice gauge vacuum. In: Fantoni S, Rosati S (eds) Condensed matter theories, vol 6. Plenum, New York

    Google Scholar 

  74. Arponen J (1983) Ann Phys (NY) 151:311

    Google Scholar 

  75. Bishop RF, Arponen J, Pajanne E (1989) Dynamic variational principles and extended coupled cluster techniques. In: Mukherjee D (ed) Aspects of many-body effects in molecules and extended systems. (Lect Notes Chem, vol 50) Springer, Berlin Heidelberg New York, p 79; Bishop RF, Arponen JS (1990) Int J Quantum Chem: Quantum Chem Symp 24:197

    Google Scholar 

  76. Bishop RF, Flynn MF, Boscá MC, Buendía E, Guardiola R (1990) J Phys G 16:L61; idem (1990) Exploring many-body theories in light nuclei. In: Greiner W, Stöcker H (eds) The nuclear equation of state, Part A: Discovery of nuclear shock waves and the EOS, Plenum, New York, p 605; idem (1990) Translationally invariant coupled cluster theory applied to the4He nucleus. In: Aguilera-Navarro VC (ed) Condensed matter theories, vol 5. Plenum, New York, p 255; Bishop RF, Buendía E, Flynn MF, Guardiola R (1990) Phys Rev C 42:1341

  77. Bishop RF, Buendía E, Flynn MF, Guardiola R (1991) Variational cluster methods in coordinate space for small systems: center of mass corrections made easy. In: Fantoni S, Rosati S (eds) Condensed matter theories, vol 6. Plenum, New York

    Google Scholar 

  78. McGarry RG (1990) PhD thesis, University of Manchester; Bishop RF, Hughes SR, McGarry RG (1990) unpublished

  79. Lipkin HJ, Meshkov N, Glick AJ (1965) Nucl Phys 62:188, 199, 211

    Google Scholar 

  80. Arponen JS, Bishop RF, Pajanne E (1987) Phys Rev A 36:2519; idem (1987) Extended coupled cluster method: quantum many-body theory made classical. In: Vashishta P, Kalia RK, Bishop RF (eds) Condensed matter theories, vol 2. Plenum, New York, p 357

    PubMed  Google Scholar 

  81. Emrich K (1981) Nucl Phys A351:379;

    Google Scholar 

  82. idem (1981) ibid A351:397;

    Google Scholar 

  83. Emrich K, Zabolitzky JG (1981) ibid A351:439

    Google Scholar 

  84. Bishop RF, Boscá MC, Flynn MF (1988) Phys Lett A132:440; idem (1989) Phys Rev A 40:3484

    Google Scholar 

  85. Bishop RF (1985) Anales Fisica A89:9; idem (1987) Towards a universal coupled cluster methodology for the various phases of condensed matter systems. In: Siemens PJ, Smith RA (eds) Recent progress in many-body theories. Texas A&M University, College Station; Bishop RF, Piechocki W, Stevens GA (1988) Few-Body Systems 4:161, 179

    Google Scholar 

  86. Bishop RF (1984) Sum rules and a coupled cluster formulation of linear response theory. In: Kümmel H, Ristig ML (eds) Recent progress in many-body theories. (Lect Notes Phys, vol 198) Springer, Berlin Heidelberg New York, p 310; idem (1984) Linear response and sum rules in the coupled cluster formalism. In: Wu SS, Kuo TTS (eds) Nucleon-nucleon interaction and nuclear-many-body problems. World Scientific, Singapore, p 604

    Google Scholar 

  87. Bijl A (1940) Physica (Utrecht) 7:869; Feynman RP (1954) Phys Rev 94:262

    Google Scholar 

  88. Goldstone J (1957) Proc Roy Soc London A239:267

    Google Scholar 

  89. Brandow B (1967) Rev Mod Phys 39:771

    Google Scholar 

  90. Offermann R, Ey W, Kümmel H (1976) Nucl Phys A273:349; Offermann R (1976) ibid A273:368; Ey W (1978) ibid A296:189

    Google Scholar 

  91. Lindgren I (1978) Int J Quantum Chem: Quantum Chem Symp 12:33

    Google Scholar 

  92. Mukherjee D (1986) Chem Phys Lett 125:207; idem (1986) Int J Quantum Chem: Quantum Chem Symp 20:409

    Google Scholar 

  93. Lindgren I, Mukherjee D (1987) Phys Rep 151:93; Chowdhuri R, Mukherjee D, Prasad MD (1989) Separability problem in general many-electron systems. In: Mukherjee D (ed) Aspects of many-body effects in molecules and extended systems (Lect Notes Chem, vol 50). Springer, Berlin Heidelberg New York, p 3

    Google Scholar 

  94. Fink M (1974) Nucl Phys A221:163

    Google Scholar 

  95. Hellmann H (1935) Acta Physicochimica USSR I(6):913; Feynman RP (1939) Phys Rev 56:340

    Google Scholar 

  96. Thouless DJ (1961) The quantum mechanics of many-body systems. Academic, New York

    Google Scholar 

  97. Kümmel HG (1983) Int J Quantum Chem 24:79

    Google Scholar 

  98. Monkhorst HJ (1977) Int J Quantum Chem: Quantum Chem Symp 11:421

    Google Scholar 

  99. Bartlett RJ (1986) in: Jørgensen P, Simon J (eds) Geometrical derivatives of energy surfaces and molecular properties. Reidel, Dordrecht, p 35; Salter EA, Trucks GW, Bartlett RJ (1989) J Chem Phys 90:1752

    Google Scholar 

  100. Scheiner AC, Scuseria GE, Rice JE, Lee TJ, Schaefer HF (1987) J Chem Phys 87:5361

    Google Scholar 

  101. Arponen JS, Bishop RF, Pajanne E (1987) Phys Rev A 36:2539

    PubMed  Google Scholar 

  102. Arponen J, Bishop RF, Pajanne E, Robinson NI (1988) Phys Rev A 37:1065; idem (1988) Towards a coupled cluster gauge-field approach to quantum hydrodynamics. In: Arponen JS, Bishop RF, Manninen M (eds) Condensed matter theories, vol 3. Plenum, New York, p 51; idem (1989) Quantum fluid dynamics: an extended coupled cluster treatment. In: Mukherjee D (ed) Aspects of many-body effects in molecules and extended systems (Lect Notes Chem, vol 50). Springer, Berlin Heidelberg New York, p 241

    PubMed  Google Scholar 

  103. Arponen J, Bishop RF, Pajanne E (1987) On an effective gauge field description of a positron impurity in polarizable media. In: Vashishta P, Kalia RK, Bishop RF (eds) Condensed matter theories, vol 2. Plenum, New York, p 373

    Google Scholar 

  104. Robinson NI, Bishop RF, Arponen J (1989) Phys Rev A 40:4256; Bishop RF, Robinson NI, Arponen J (1990) Extended coupled cluster techniques for excited states: applications to quasispin models. In: Aguilera-Navarro VC (ed) Condensed matter theories, vol 5. Plenum, New York, p 329

    PubMed  Google Scholar 

  105. Arponen JS, Bishop RF (1990) Phys Rev Lett 64:111;

    PubMed  Google Scholar 

  106. idem (1990) Coupled cluster parametrizations of model field theories and their Bargmann-space representations. In: Avishai Y (ed) Recent progress in many-body theories, vol 2. Plenum, New York;

    Google Scholar 

  107. Aalto E, Arponen JS, Bishop RF (1990) On the Bargmann space approach to the extended coupled cluster method for simple anharmonic systems. In: Aguilera-Navarro VC (ed) Condensed matter theories, vol 5. Plenum, New York, p 297;

    Google Scholar 

  108. Arponen JS, Bishop RF (1991) Ann Phys (NY) 207:171;

    Google Scholar 

  109. idem (1991) Theor Chim Acta 80

  110. Arponen JS (1991) Theor Chim Acta 80

  111. Altenbokum M, Emrich K, Kümmel H, Zabolitzky JG (1987) A temperature dependent coupled cluster method. In: Vashishta P, Kalia RK, Bishop RF (eds) Condensed matter theories, vol 2. Plenum, New York, p 389

    Google Scholar 

  112. Moszkowski SA (1988) Role of virtual double delta components in nuclei. In: Arponen JS, Bishop RF, Manninen M (eds) Condensed matter theories, vol 3. Plenum, New York, p 269

    Google Scholar 

  113. Zabolitzky JG, Ey W (1979) Nucl Phys A328:507

    Google Scholar 

  114. Day B (1981) Phys Rev Lett 47:226; Day B, Zabolitzky JG (1981) Nucl Phys A366:221

    Google Scholar 

  115. Kümmel HG (1979) Nucl Phys A317:199

    Google Scholar 

  116. Bishop RF, Lührmann KH (1978) Phys Rev B 17:3757;

    Google Scholar 

  117. idem (1982) ibid Phys Rev B 26:5523;

    Google Scholar 

  118. idem (1978) unpublished

  119. Foldy LL (1961) Phys Rev 124:649; idem (1962) ibid 125:2208

    Google Scholar 

  120. Brueckner KA (1967) Phys Rev 156:204

    Google Scholar 

  121. Zabolitzky JG (1980) Phys Rev B 22:2353

    Google Scholar 

  122. Emrich K, Zabolitzky JG (1984) Phys Rev B 30:2049

    Google Scholar 

  123. Ceperley DM, Alder BJ (1980) Phys Rev Lett 45:566; Vosko SH, Wilk L, Nusair M (1980) Can J Phys 58:1200

    Google Scholar 

  124. Vashishta P, Singwi KS (1972) Phys Rev B 6:875, (E)4883

    Google Scholar 

  125. Freeman DL (1977) Phys Rev B 15:5512; Arponen J, Pajanne E (1982) J Phys C 15:2665, 2683

    Google Scholar 

  126. Bishop RF, Lahoz WA (1987) J Phys A 20:4203; Lahoz WA, Bishop RF (1988) Z Phys B 73:363

    Google Scholar 

  127. Lieb EH, Liniger W (1963) Phys Rev 130:1605;

    Google Scholar 

  128. idem (1963) ibid Phys Rev 130:1616

    Google Scholar 

  129. Agassi D, Lipkin HG, Meshkov N (1966) Nucl Phys 86:321

    Google Scholar 

  130. Lührmann KH (1977) Ann Phys (NY) 103:253

    Google Scholar 

  131. Arponen J (1982) J Phys G 8:L129; Arponen J, Rantakivi J (1983) Nucl Phys A407:141

  132. Giradeau M (1960) J Math Phys 1:516

    Google Scholar 

  133. Bethe HA (1931) Z Phys 71:205

    Google Scholar 

  134. Hughes SR (1990) PhD thesis, University of Manchester

  135. Bender CM, Wu TT (1969) Phys Rev 184:1231; idem (1973) Phys Rev D 7:1620; Simon B (1970) Ann Phys (NY) 58:76

    Google Scholar 

  136. Hsue CS, Chern JL (1984) Phys Rev D 29:643

    Google Scholar 

  137. Kümmel H (1986) Preparing the ground for coupled cluster calculations. In: Malik FB (ed) Condensed matter theories, vol 1. Plenum, New York p 33

    Google Scholar 

  138. Kaulfuss UB, Altenbokum M (1986) Phys Rev D 33:3658

    Google Scholar 

  139. Kümmel HG (1988) The anharmonic oscillator revisited. In: Arponen JS, Bishop RF, Manninen M (eds) Condensed matter theories, vol 3. Plenum, New York, p 21

    Google Scholar 

  140. Bishop RF, Flynn MF (1988) Phys Rev A 38:2211

    PubMed  Google Scholar 

  141. Kaulfuss U (1985) Phys Rev D 32:1421; Hsue CS, Kümmel H, Ueberholz P (1985) ibid 32:1435; Altenbokum M, Kümmel H (1985) ibid 32:2014; Kaulfuss U, Altenbokum M (1987) ibid 35:609; Funke M, Kaulfuss U, Kümmel H (1987) ibid 35:621

    Google Scholar 

  142. Kümmel H (1983) Phys Rev C 27:765; Hasberg G, Kümmel H (1986) ibid 33:1367

    Google Scholar 

  143. Anderson PW (1987) Science 235:1196

    Google Scholar 

  144. Roger M, Hetherington JH (1990) Phys Rev B 41:200

    Google Scholar 

  145. Bishop RF, Parkinson JB, Yang Xian (1991) Phys Rev B 43:13782; idem (1991) Theor Chim Acta 80:181

    Google Scholar 

  146. Haldane FDM (1983) Phys Lett A93:464; Affleck I, Haldane FDM (1987) Phys Rev B 36:5291

    Google Scholar 

  147. Gross EP (1958) Ann Phys (NY) 4:57; idem (1961) Nuovo Cim 20:454; Pitaevskii LP (1961) Sov Phys — JETP 13:451; Fetter AL, Walecka JD (1971) Quantum theory of many-particle systems. McGraw-Hill, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Manchester Institute of Science and Technology, P.O. Box 88, M60 1QD, Manchester, UK

    R. F. Bishop

Authors
  1. R. F. Bishop
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bishop, R.F. An overview of coupled cluster theory and its applications in physics. Theoret. Chim. Acta 80, 95–148 (1991). https://doi.org/10.1007/BF01119617

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01119617

Key words

Search

Navigation