Abstract.
The present paper intends to present an extension of the constrained-path quantum Monte Carlo approach allowing to reconstruct non-yrast states in order to reach the complete spectroscopy of nuclei within the interacting shell model. As in the yrast case studied in a previous work, the formalism involves a variational symmetry-restored wave function assuming two central roles. First, it guides the underlying Brownian motion to improve the efficiency of the sampling. Second, it constrains the stochastic paths according to the phaseless approximation to control sign or phase problems that usually plague fermionic QMC simulations. Proof-of-principle results in the sd valence space are reported. They prove the ability of the scheme to offer remarkably accurate binding energies for both even- and odd-mass nuclei irrespective of the considered interaction.
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References
M. Troyer, U. Wiese, Phys. Rev. Lett. 64, 170210 (2005)
D.M. Ceperley, M.H. Kalos, in Monte Carlo Methods in Statistical Physics, edited by K. Binder, 1st edition (Springer-Verlag, New York, 1979)
M.H. Kalos, D. Levesque, L. Verlet, Phys. Rev. A 9, 2178 (1974)
J.G. Zabolitsky, M.H. Kalos, Nucl. Phys. A 356, 114 (1981)
R.C. Grimm, R.G. Storer, J. Comput. Phys. 7, 134 (1971)
J.B. Anderson, J. Chem. Phys. 65, 4122 (1976)
W.M.C. Foulkes, L. Mitas, R.J. Needs, G. Rajagopal, Rev. Mod. Phys. 73, 33 (2001)
R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995)
D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45, 566 (1980)
P.J. Reynolds, D.M. Ceperley, B.J. Alder, W.A. Lester, J. Chem. Phys. 77, 5562 (1982)
B. Tanatar, D.M. Ceperley, Phys. Rev. B 39, 5005 (1989)
G. Ortiz, D.M. Ceperley, R.M. Martin, Phys. Rev. Lett. 71, 2777 (1993)
S.C. Pieper, R.B. Wiringa, Annu. Rev. Nucl. Part. Sci. 51, 53 (2001) and references therein
J. Carlson, J. Morales jr., V.R. Pandharipande, D.G. Ravenhall, Phys. Rev. C 68, 025802 (2003)
E. Lusk, S.C. Pieper, R. Butler, SciDAC Rev. 17, 30 (2010)
K.E. Schmidt, S. Fantoni, Phys. Lett. B 446, 99 (1999)
S. Gandolfi, F. Pederiva, S. Fantoni, K.E. Schmidt, Phys. Rev. Lett. 99, 022507 (2007)
A. Gezerlis, I. Tews, E. Epelbaum, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, Phys. Rev. Lett. 111, 032501 (2013)
R.D. Stratonovich, Sov. Phys. Dokl. 2, 416 (1958)
J. Hubbard, Phys. Rev. Lett. 3, 77 (1959)
G. Sugiyama, S.E. Koonin, Ann. Phys. (N.Y.) 168, 1 (1986)
F.F. Assaad, in Lecture notes of the Winter School on Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, edited by J. Grotendorst, D. Marx, A. Muramatsu, Vol. 10 (Publication Series of the John von Neumann Institute for Computing, 2002) p. 99
S. Zhang, J. Carlson, J.E. Gubernatis, Phys. Rev. B 55, 7464 (1997)
S. Zhang, in Theoretical Methods for Strongly Correlated Electron Systems, edited by D. Sénéchal, A.-M. Tremblay, C. Bourbonnais (Springer, 2003) and references therein
S. Zhang, H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003)
W.A. Al-Saidi, S. Zhang, H. Krakauer, J. Chem. Phys. 124, 224101 (2006)
W. Purwanto, H. Krakauer, S. Zhang, Phys. Rev. B 80, 214116 (2009)
E. Caurier, G. Martínez-Pinedo, F. Nowacki, A. Poves, A.P. Zuker, Rev. Mod. Phys. 77, 427 (2005)
S.E. Koonin, D.J. Dean, K. Langanke, Phys. Rep. 278, 1 (1997) and references therein
K. Langanke, D.J. Dean, P.B. Radha, Y. Alhassid, S.E. Koonin, Phys. Rev. C 52, 718 (1995)
J.A. White, S.E. Koonin, D.J. Dean, Phys. Rev. C 61, 034303 (2000)
Y. Alhassid, L. Fang, H. Nakada, Phys. Rev. Lett. 101, 082501 (2008)
K. Langanke, D.J. Dean, S.E. Koonin, P.B. Radha, Nucl. Phys. A 613, 253 (1997)
P.B. Radha, D.J. Dean, S.E. Koonin, T.T.S. Kuo, J. Retamosa, P. Vogel, Phys. Rev. Lett. 76, 2642 (1996)
C. Özen, K. Langanke, G. Martinez-Pinedo, D.J. Dean, Phys. Rev. C 75, 064307 (2007)
K. Langanke, Nucl. Phys. A 778, 233 (2006)
C. Özen, Y. Alhassid, H. Nakada, Phys. Rev. C 91, 034329 (2015)
Y. Alhassid, M. Bonett-Matiz, S. Liu, H. Nakada, Phys. Rev. C 92, 024307 (2015)
G.H. Lang, C.W. Johnson, S.E. Koonin, W.E. Ormand, Phys. Rev. C 48, 1518 (1993)
Y. Alhassid, D.J. Dean, S.E. Koonin, G. Lang, W.E. Ormand, Phys. Rev. Lett. 72, 613 (1994)
G. Puddu, Eur. Phys. J. A 9, 171 (2000)
G. Puddu, Phys. Rev. C 67, 051304 (2003)
G. Puddu, Eur. Phys. J. A 21, 227 (2004)
G. Puddu, Acta Phys. Pol. B 35, 2121 (2004)
M. Honma, T. Mizusaki, T. Otsuka, Phys. Rev. Lett. 77, 3315 (1996)
N. Shimizu, T. Abe, Y. Tsunoda, Y. Utsuno, T. Yoshida, T. Mizusaki, M. Honma, T. Otsuka, Prog. Theor. Exp. Phys. 2012, 01A205 (2012) and references therein
T. Otsuka, M. Honma, T. Mizusaki, N. Shimizu, Y. Utsuno, Prog. Part. Nucl. Phys. 47, 319 (2001)
T. Mizusaki, T. Otsuka, Y. Utsuno, M. Honma, T. Sebe, Phys. Rev. C 59, R1846 (1999)
T. Otsuka, Y. Utsuno, T. Mizusaki, M. Honma, Nucl. Phys. A 682, 155 (2001)
L. Liu, T. Otsuka, N. Shimizu, Y. Utsuno, R. Roth, Phys. Rev C 86, 014302 (2012)
J. Bonnard, O. Juillet, Phys. Rev. Lett. 111, 012502 (2013)
H.F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959)
M. Suzuki, Commun. Math. Phys. 51, 183 (1976)
S. Zhang, in Emergent Phenomena in Correlated Matter: Modeling and Simulation, edited by E. Pavarini, E. Koch, U. Schollwöck, Vol. 3 (2013) http://www.cond-mat.de/events/correll13 (OpenAccess Book)
J. Bonnard, O. Juillet, to be published in J. Phys.: Conf. Ser
C.W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1983)
F. Villars, in Proceedings of the International School of Physics “Enrico Fermi”, Course XXXVI, Many-body Description of Nuclear Structure and Reactions, edited by C. Bloch (Academic Press, New York, 1966)
A. Messiah, Quantum Mechanics, Vol. 2 (Dunod, Paris, 2003)
H. Shi, C.A. Jiménez-Hoyos, R. Rodríguez-Guzmán, G.E. Scuseria, S. Zhang, Phys. Rev. B 89, 125129 (2014)
H. Shi, S. Zhang, Phys. Rev. B 88, 125132 (2013)
K.W. Schmid, Prog. Part. Nucl. Phys. 52, 565 (2013) and references therein
J.P. Blaizot, G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, Mass., 1986)
B.H. Wildenthal, Prog. Part. Nucl. Phys. 11, 5 (1984)
B.A. Brown, Prog. Part. Nucl. Phys. 47, 517 (2001)
M. Pervin, S.C. Pieper, R.B. Wiringa, Phys. Rev. C 76, 064319 (2007)
M.C. Buonaura, S. Sorella, Phys. Rev. B 57, 11446 (1998)
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Bonnard, J., Juillet, O. Constrained-path quantum Monte Carlo approach for non-yrast states within the shell model. Eur. Phys. J. A 52, 110 (2016). https://doi.org/10.1140/epja/i2016-16110-6
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DOI: https://doi.org/10.1140/epja/i2016-16110-6