Abstract
A description of correlated basis function theory for Fermi systems is given with the perspective of discussing some of the recent developments and its range of applications. The actual status of variational calculations in liquid helium, strongly correlated electrons and nuclear matter is presented, by discussing the merits and limitations of the most realistic trial wave functions. Correlated basis function perturbation theory is described as a tool to go beyond variational calculations. The not-orthogonal and the newly developed orthogonal versions are discussed and compared. A brief review of the one-body Green’s function calculation in nuclear matter is presented, as one of the main applications of the orthogonal version of the perturbation theory. We describe a generalized Fermi Hyper-Netted Chain scheme, showing that it constitutes a powerful method to compute the hamiltonian and identity operator matrix elements, which enter the correlated basis theory, starting from its zeroth order or variational theory. Such scheme sums up both reducible and irreducible cluster terms, whereas the original FHNC one takes care of the irreducible terms only, and it is particularly suitable for calculations with state dependent correlations, as well as for finite systems, like nuclei and helium droplets.
Preview
Unable to display preview. Download preview PDF.
References
D.D. Osheroff, R.C. Richardson and D.M. Lee, Phys. Rev. Lett. 28, 885 (1972)
S. Fantoni and S. Rosati, Lett. Nuovo Cimento 10, 545 (1974)
E. Krotscheck and M.L. Ristig, Phys. Lett. A48, 17 (1971)
W.L. McMillan, Phys. Rev. A 138, 442 (1965)
D.M. Ceperley and M.H. Kalos, Monte Carlo Methods in Statistical Physics edited by K. Binder, 1979 (Springer-Verlag, Berlin)
E. Krotscheck, Phys. Rev. B 33, 3158 (1986)
E. Krotscheck, contribution to this volume
S.A. Vitiello and K.E. Schmidt, Phys. Rev. B 46, 5442 (1992)
S. Moroni, S. Fantoni and G. Senatore, Phys. Rev. B 52, 13547 (1995)
J.W. Clark, Progress in Particle and Nuclear Physics 2, edited by D.H. Wilkinson, 1979 (Pergamon, Oxford) 89
E. Krotscheck and J.W. Clark, Nucl. Phys. A333, 77 (1980)
S. Fantoni and V.R. Pandharipande, Phys. Rev. C 37, 1697 (1988)
R.F. Bishop, contribution to this volume
K.E. Schmidt and M.H. Kalos, Monte Carlo Methods in Statistical Physics II, Topics in Current Physics, edited by K. Binder, 1984 (Springer-Verlag, Berlin)
K.E. Schmidt and D.M. Ceperley, Monte Carlo Methods III, edited by K. Binder, 1991 (Springer-Verlag, Berlin)
D.M. Ceperley, Rev. Mod. Phys. 67, 279 (1995)
S. Fantoni and S. Moroni, Many Body Theory of Correlated Fermion Systems, edited by J.M. Arias, M. Gallardo and M. Lozano, 1998 (World Scientific), in press
A. Fabrocini, contribution to this volume
J.G. Zabolitzky, Phys. Rev. B 22, 2353 (1980)
E. Krotscheck, Ann. Phys. (NY) 155, 1 (1984)
M.L. Ristig, J.W. Kim and R. Mehlman, Condensed Matter Theories, Vol. 11, edited by E. Ludeña et al, 1995 (Nova Science Publishers, New York)
V.R. Pandharipande and R.B. Wiringa, Rev. Mod. Phys. 51, 821 (1979)
S. Rosati, in International School of Physics Enrico Fermi, Course LXXIX, edited by A. Molinari, 1981 (North-Holland, Amsterdam), 73
J.G. Zabolitzky, in Advances in Nuclear Physics, Vol. 12, edited by J.W. Negele and E. Vogt, 1981 (Plenum, New York, London) 1
J.P. Blaizot and G. Ripka, Quantum Theory of Finite Systems, 1986 (The MIT Press, Cambridge)
A. Fabrocini and S. Fantoni, First International Course on Condensed Matter, ACIF series, Vol. 8 edited by D. Prosperi, S. Rosati and S. Violini, 1987 (World Scientific, Singapore), 87
V.R. Pandharipande, I. Sick and P.K.A. de Witt Huberts, Rev. Mod. Phys. 69, 981 (1997)
E. Feenberg, Theory of Quantum Liquids, edited by K. Binder, 1969 (Springer, New York)
S. Moroni, G. Senatore and S. Fantoni, Phys. Rev. B. 55, 1040 (1997)
S. Fantoni and V.R. Pandharipande, Nucl. Phys. A427, 473 (1984)
O. Benhar, A. Fabrocini and S. Fantoni, 4th Workshop on Perspectives in Nuclear Physics at Intermediate Energies, edited by S. Boffi, C. Ciofi degli Atti and M. Giannini, 1989 (World Scientific, Singapore), 333
R.A. Aziz et al, J. Chem. Phys. 70, 4330 (1979)
M.H. Kalos et al, Phys. Rev. B 24, 115 (1981)
K.E. Schmidt et al, Phys. Rev. Lett. 47, 807 (1981)
E. Manousakis et al, Phys. Rev. B 28, 3770 (1983)
R.P. Feynman and M. Cohen, Phys. Rev. 102 1189 (1956)
M. Viviani et al, Phys. Rev. B 38, 4523 (1988)
J.W. Lawson et al, Phys. Rev. Lett. 78, 1846 (1997)
O. Ciftja, PhD thesis, International School for Advanced Studies, Trieste (1997)
F. Pederiva et al, Phys. Rev. B 53, 15129 (1996)
K.E. Schmidt, private communication
Q.N. Usmani, S. Fantoni and V.R. Pandharipande, Phys. Rev. B 26, 6123 (1983)
A. Fabrocini and S. Rosati, Nuovo Cimento D 1, 165; 567 (1982)
S.A. Vitiello et al, Phys. Rev. Lett. 60, 1970 (1988)
L. Reatto and G.L. Masserini, Phys. Rev. B 38, 4516 (1988)
F. Pederiva et al, Phys. Rev. Lett. 72, 2589 (1994)
S. Moroni, L. Reatto and S. Fantoni, Czech. J. Phys. S1 46 281 (1996)
D.C. Tsui, H.L. Stormer and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)
P.W. Anderson, Science 235, 1196 (1987)
R.B. Laughlin, The Quantum Hall Effect, edited by R. Prange and S. Girvin, 1987 (Springer-Verlag, New York)
T. Chakraborty and P. Pietaläinen, The Fractional Quantum Hall Effect, 1988 (Springer-Verlag, New York)
R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)
B.I. Halperin, Helv. Phys. Acta 56, 75 (1983)
J.M. Caillol et al, J. Stat. Phys. 28, 325 (1982)
J.P. Hansen and D. Levesque, J. Phys. C 14, L603 (1981)
O. Ciftja and S. Fantoni, Europhys. Lett. 36, 663 (1996)
J.K. Jain, Phys. Rev. Lett. 63, 199 (1989)
G. Dev and J.K. Jain, Phys. Rev. Lett. 69, 2483 (1992)
X.G. Wu, G. Dev and J.K. Jain, Phys. Rev. Lett. 71, 153 (1993)
O. Ciftja and S. Fantoni, Phys. Rev. B 56, 6712 (1997)
J.K. Jain and R.K. Kamilla, Phys. Rev. B 55, R4895 (1997)
O. Ciftja et al, J. Low Temp. Phys. 108, 357 (1997)
J.G. Bednorz and K.A. MĂĽller, Z. Phys. B 64, 188 (1986)
C.W. Chu et al, Phys. Rev. Lett. 58, 405 (1987)
D. Vollhardt, Rev. Mod. Phys. 99, 1196 (1984)
E. Manousakis, Rev. Mod. Phys. 63, 1 (1991)
E.H. Lieb and F.Y. Wu, Phys. Rev. Lett. 20, 1445 (1968)
S. Fantoni et al, Physica C 153–155, 1255 (1988)
W. Metzner and D. Vollhardt, Phys. Rev. Lett. 59, 121 (1987)
X.Q. Wang et al, Phys. Rev. B 41, 11479 (1990)
X.Q. Wang et al, Phys. Rev. B 46, 8894 (1992)
P. Fazekas and K. Penc, Int. J. Mod. Phys. B 1, 1021 (1988)
H. Yokoyama and H. Shiba, J. Phys. Soc. Jap. 56, 1490; 3570; 3582 (1987)
J. Solyom, Adv. Phys. 28, 201 (1979)
F.C. Zhang et al, Supercond. Sci. Technol. 1, 36 (1988)
G. Kotliar and J. Liu, Phys. Rev. B 38, 5142 (1988)
J.R. Schrieffer, X.G. Wen and S.C. Zhang, Phys. Rev. B 39, 11663 (1989)
R.V. Reid Jr., Ann. Phys. (N.Y.) 50, 411 (1968)
M. Lacombe et al, Phys. Rev. C 21, 861 (1980)
I.E. Lagaris and V.R. Pandharipande, Nucl. Phys. A359, 331 (1981)
R.B. Wiringa, V.G.J. Stocks and R. Schiavilla, Phys. Rev. C 51, 38 (1995)
J.L. Forest et al, Phys. Rev. C 54, 646 (1996)
A. Akmal and V.R. Pandharipande, Phys. Rev. C 56, 2261 (1997)
R. Schiavilla, V.R. Pandharipande and R.B. Wiringa, Nucl. Phys. A449, 219 (1986)
J. Fujita and H. Miyazawa, Prog. Theor. Phys. 17, 360 (1957)
B.S. Pudliner, Ph.D. Thesis, University of Illinois at Urbana-Champaign (1996)
B.S. Pudliner et al, Phys. Rev. Lett. 74, 4396 (1995)
A. Kievsky, S. Rosati and M. Viviani Nucl. Phys. A57, 511 (1994)
M. Viviani, R. Schiavilla and A. Kievsky, Phys. Rev. C 54, 534 (1996)
E. Fradkin, Field Theories of Condensed Matter Systems, 1991 (Addison-Wesley, Reading MA)
P.M. Morse and H. Feshbach, Methods of Theoretical Physics, 1953 (McGraw-Hill, New York), Chap. 9, Part II
S. Fantoni, Phys. Rev. B 29, 2544 (1984)
C.W. Woo, Phys. Rev. 151, 138 (1966)
J.W. Clark, Lecture Notes in Physics, 138, edited by R. Guardiola and J. Ros, 1981 (Springer, New York), p. 184
E. Krotscheck, R.A. Smith and J.W. Clark, Lecture Notes in Physics, 142, 1981 (Springer, New York), 270
E. Krotscheck, R.A. Smith and A.D. Jackson, Phys. Lett. B 104, 421 (1981)
A.D. Jackson et al, Nucl. Phys. A386, 125 (1982)
E. Manousakis and V.R. Pandharipande, Phys. Rev. B 33, 150 (1986)
E. Krotscheck, R.A. Smith, J.W. Clark, and R.M. Panoff, Phys. Rev. B 24, 6383 (1981)
S. Fantoni, V.R. Pandharipande and K.E. Schmidt, Phys. Rev. Lett. 48, 878 (1982)
B.L. Friman and E. Krotscheck, Phys. Rev. Lett. 49, 1705 (1982)
R.B. Wiringa, R.A. Smith and T.L. Ainsworth, Phys. Rev. C 29, 1207 (1984)
I.E. Lagaris and V.R. Pandharipande, Nucl. Phys. A359, 349 (1981)
S. Fantoni, B.L. Friman and V.R. Pandharipande, Nucl. Phys. A399, 51 (1983)
A. Fabrocini and S. Fantoni, Phys. Lett. B 298, 263 (1993)
A.A. Abrikosov, L.P. Gorkov and I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, 1963 (Dover, New Jork)
M. Baldo et al, Nucl. Phys. A545, 741 (1992)
M. Bauer et al, J. Phys. G 8, 525 (1982)
E. Krotscheck, Phys. Rev. A 26, 3536 (1982)
S. Fantoni, B.L. Friman and V.R. Pandharipande, Phys. Lett. B 104, 89 (1981)
J.W. Negele and K. Yazaki, Phys. Rev. Lett. 47, 71 (1981)
A.B. Migdal, JETP (Sov. Phys.) 5, 333 (1957)
J.M. Luttinger, Phys. Rev. 119, 1153 (1960)
O. Benhar, A. Fabrocini and S. Fantoni, Phys. Rev. C 41, R24 (1990)
O. Benhar, A. Fabrocini and S. Fantoni, Nucl. Phys. A505, 267 (1989)
P.O. Löwdin, J. Chem. Phys. 18, 365 (1950)
H. Brandow and H. Baird, Rev. Mod. Phys. 39, 771 (1967)
A. Fabrocini and S. Fantoni, Nucl. Phys. A503, 375 (1989)
A. Fabrocini et al, Phys. Rev. B 33, 6057 (1986)
A. Fabrocini et al, Phys. Rev. B 54, 1035 (1996)
S. Fantoni and S. Rosati, Nuovo Cimento, A 20, 179 (1974)
T. Morita, Progr. Theor. Phys. 20, 920 (1958)
J.M. Van Leeuwen, J. Groeneveld and J. De Boer, Physica, 25, 792 (1959)
S. Fantoni and S. Rosati, Phys. Lett. B 84, 23 (1979)
T. Morita and K. Hiroike, Progr. Theor. Phys. 23, 1003 (1960)
S. Fantoni, Nuovo Cimento, A 44, 191 (1978)
G. CĂł et al, Nucl. Phys. A549, 439 (1992)
F. Arias de Saavedra et al, Nucl. Phys. A605, 359 (1996)
A. Fabrocini et al, Phys. Rev. C (1998) in press
R.B. Wiringa, V. Fiks and A. Fabrocini, Phys. Rev. C 38, 1010 (1988)
I.E. Lagaris, Anales de Fisica, 81, 39 (1985)
G.E. Brown, Many Body Physics, 1972 (North-Holland, Amsterdam)
A.L. Fetter and J.D. Walecka, Quantum Theory of Many-Particle Systems, 1971 (McGraw-Hill, NY)
P.K.A. DeWitt Huberts, J. Phys. G 16, 507 (1990)
S. Frullani and J. Mougey, Adv. Nucl. Phys. 14, 1 (1984)
O. Benhar, A. Fabrocini and S. Fantoni, Nucl. Phys. A550, 201 (1992)
B. Frois and I. Sick, editors Modern Topics in Electron Scattering, (1991) (World Scientific, Singapore)
S. Fantoni and V.R. Pandharipande, Nucl. Phys. A473, 234 (1987)
A.S. Rinat and W.H. Dickhoff, Phys. Rev. B 42, 1004 (1990)
O. Benhar et al, Phys. Rev. C 44, 2328 (1991)
S. Fantoni and I. Sick, Electron-Nucleus Scattering, edited by O. Benhar, A. Fabrocini and R. Schiavilla, 1994 (World Scientific, Singapore), 88–120
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag
About this paper
Cite this paper
Fantoni, S., Fabrocini, A. (1998). Correlated basis function theory for fermion systems. In: Navarro, J., Polls, A. (eds) Microscopic Quantum Many-Body Theories and Their Applications. Lecture Notes in Physics, vol 510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104526
Download citation
DOI: https://doi.org/10.1007/BFb0104526
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64471-2
Online ISBN: 978-3-540-69787-9
eBook Packages: Springer Book Archive