Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree-Fock-Bogoliubov wavefunctions. (English) Zbl 1372.82045
The main purpose is to introduce a quantum Monte Carlo theoretical approach for the computation of an approximate ground state of strongly correlated superconducting fermions. This framework relies on Hartree-Fock-Bogoliubov that undergo a Brownian motion in imaginary time. The efficiency of this approach is improved by guiding the dynamics to generate walkers according to the importance of their overlap with a trial wavefunction.
Reviewer: Vicenţiu D. Rădulescu (Craiova)
MSC:
| 82D55 | Statistical mechanics of superconductors |
| 65C05 | Monte Carlo methods |
| 82B31 | Stochastic methods applied to problems in equilibrium statistical mechanics |
| 82B80 | Numerical methods in equilibrium statistical mechanics (MSC2010) |
| 82D50 | Statistical mechanics of superfluids |
| 60J65 | Brownian motion |
Keywords:
strong correlations; superconductivity; superfluidity; stochastic approaches; Hartree-Fock-Bogoliubov wavefunctionsReferences:
| [1] | Kamerlingh Onnes H 1911 Proc. K. Ned. Akad. Wet.13 1274 |
| [2] | Kamerlingh Onnes H 1911 Proc. K. Ned. Akad. Wet.14 113 |
| [3] | Matthias B T, Geballe T H, Willens R H, Corenzwit E and Hull G W 1965 Phys. Rev.139 A1501 · doi:10.1103/PhysRev.139.A1501 |
| [4] | Drozdov A P, Eremets M I, Troyan I A, Ksenofontov V and Shylin S I 2015 Nature525 73 · doi:10.1038/nature14964 |
| [5] | Thalmeier P, Zwicknagl G, Stockert O, Sparn G and Steglich F 2005 Frontiers in Superconducting Materials ed A V Narlikar (Berlin: Springer) p 109 · doi:10.1007/3-540-27294-1_3 |
| [6] | Jourdan M, Huth M and Adrian H 1999 Nature398 47 · doi:10.1038/17977 |
| [7] | Yuan H Q, Grosche F M, Deppe M, Geibel C, Sparn G and Steglich F 2003 Science302 2104 · doi:10.1126/science.1091648 |
| [8] | Bruls G et al 1994 Phys. Rev. Lett.72 1754 · doi:10.1103/PhysRevLett.72.1754 |
| [9] | Himeda A, Kato T and Ogata M 2002 Phys. Rev. Lett.88 117001 · doi:10.1103/PhysRevLett.88.117001 |
| [10] | Raczkowski M, Capello M, Poilblanc D, Frésard R and Oleś A M 2007 Phys. Rev. B 76 140505 · doi:10.1103/PhysRevB.76.140505 |
| [11] | Hamidian M H et al 2016 Nature532 343 · doi:10.1038/nature17411 |
| [12] | Fradkin E, Kivelson S A and Tranquada J M 2015 Rev. Mod. Phys.87 457 · doi:10.1103/RevModPhys.87.457 |
| [13] | Leprévost A, Juillet O and Frésard R 2015 New J. Phys.17 103023 · doi:10.1088/1367-2630/17/10/103023 |
| [14] | Ren Z-H et al 2008 Europhys. Lett.83 17002 · doi:10.1209/0295-5075/83/17002 |
| [15] | Maeno Y, Rice T M and Sigrist M 2001 Phys. Today54 42 · doi:10.1063/1.1349611 |
| [16] | Giamarchi T and Lhuillier C 1991 Phys. Rev. B 43 12943 · doi:10.1103/PhysRevB.43.12943 |
| [17] | Misawa T and Imada M 2014 Phys. Rev. B 90 115137 · doi:10.1103/PhysRevB.90.115137 |
| [18] | Hirsch J E 1985 Phys. Rev. B 31 4403 · doi:10.1103/PhysRevB.31.4403 |
| [19] | White S R, Scalapino D J, Sugar R L, Loh E Y, Gubernatis J E and Scalettar R T 1989 Phys. Rev. B 40 506 · doi:10.1103/PhysRevB.40.506 |
| [20] | Meng Z Y, Lang T C, Wessel S, Assaad F F and Muramatsu A 2010 Nature464 847 · doi:10.1038/nature08942 |
| [21] | Sorella S, Otsuka Y and Yunoki S 2012 Sci. Rep.2 992 · doi:10.1038/srep00992 |
| [22] | Grover T 2013 Phys. Rev. Lett.111 130402 · doi:10.1103/PhysRevLett.111.130402 |
| [23] | Assaad F F, Lang T C and Toldin F P 2014 Phys. Rev. B 89 125121 · doi:10.1103/PhysRevB.89.125121 |
| [24] | Troyer M and Wiese U 2005 Phys. Rev. Lett.94 170210 · doi:10.1103/PhysRevLett.94.170201 |
| [25] | Ceperley D M and Alder B J 1980 Phys. Rev. Lett.45 566 · doi:10.1103/PhysRevLett.45.566 |
| [26] | Reynolds P J, Ceperley D M, Alder B J and Lester W A Jr 1982 J. Chem. Phys.77 5593 · doi:10.1063/1.443766 |
| [27] | Foulkes W M C, Mitas L, Needs R J and Rajagopal G 2001 Rev. Mod. Phys.73 33 · doi:10.1103/RevModPhys.73.33 |
| [28] | Wu C and Zhang S-C 2005 Phys. Rev. B 71 155115 · doi:10.1103/PhysRevB.71.155115 |
| [29] | Zhang S, Carlson J and Gubernatis J E 1995 Phys. Rev. Lett.74 3652 · doi:10.1103/PhysRevLett.74.3652 |
| [30] | Zhang S 1999 Phys. Rev. Lett.83 2777 · doi:10.1103/PhysRevLett.83.2777 |
| [31] | Zhang S and Krakauer H 2003 Phys. Rev. Lett.90 136401 · doi:10.1103/PhysRevLett.90.136401 |
| [32] | Anderson J B 1975 J. Chem. Phys.63 1499 · doi:10.1063/1.431514 |
| [33] | Blaizot J-P and Ripka G 1985 Quantum Theory of Finite Systems (Cambridge, MA: The MIT Press) |
| [34] | Ring P and Schuck P 2003 The Nuclear Many-Body Problem (Berlin: Springer) |
| [35] | Zhang W, Feng D H and Gilmore R 1990 Rev. Mod. Phys.62 867 · doi:10.1103/RevModPhys.62.867 |
| [36] | Bloch C and Messiah A 1962 Nucl. Phys.39 95 · Zbl 0127.45701 · doi:10.1016/0029-5582(62)90377-2 |
| [37] | Zumino B 1962 J. Math. Phys.3 1055 · Zbl 0114.25201 · doi:10.1063/1.1724294 |
| [38] | Sugiyama G and Koonin S E 1986 Ann. Phys.168 1 · doi:10.1016/0003-4916(86)90107-7 |
| [39] | Hirsch J E 1983 Phys. Rev. B 28 4059 · doi:10.1103/PhysRevB.28.4059 |
| [40] | Carusotto I, Castin Y and Dalibard J 2001 Phys. Rev. A 63 023606 · doi:10.1103/PhysRevA.63.023606 |
| [41] | Juillet O and Chomaz Ph 2003 Phys. Rev. Lett.88 142503 · doi:10.1103/PhysRevLett.88.142503 |
| [42] | Juillet O, Gulminelli F and Chomaz Ph 2004 Phys. Rev. Lett.92 160401 · doi:10.1103/PhysRevLett.92.160401 |
| [43] | Al-Saidi W A, Zhang S and Krakauer H 2006 J. Chem. Phys.124 224101 · doi:10.1063/1.2200885 |
| [44] | Wouters S, Verstichel B, Van Neck D and Kin-Lic Chan G 2014 Phys. Rev. B 90 045104 · doi:10.1103/PhysRevB.90.045104 |
| [45] | Bonnard J and Juillet O 2013 Phys. Rev. Lett.111 012502 · doi:10.1103/PhysRevLett.111.012502 |
| [46] | Bonnard J and Juillet O 2016 Eur. Phys. J. A 52 110 · doi:10.1140/epja/i2016-16110-6 |
| [47] | Zhang S 2013 Emergent Phenomena in Correlated Matter Modeling and Simulation(Verlag des Forschungszentrum Jülich vol 3) ed E Pavarini et al (Jülich: Forschungszentrum Jülich GmbH) pp 449-81 |
| [48] | Lang G H, Johnson C W, Koonin S E and Ormand W E 1993 Phys. Rev. C 48 1518 · doi:10.1103/PhysRevC.48.1518 |
| [49] | Gardiner C W 1983 Handbook of Stochastic Methods (Berlin: Springer) · Zbl 0515.60002 · doi:10.1007/978-3-662-02377-8 |
| [50] | Corney J F and Drummond P D 2006 Phys. Rev. B 73 125112 · doi:10.1103/PhysRevB.73.125112 |
| [51] | Bonnard J 2012 Approches Monte-Carlo quantiques à chemins contraints pour le modèle en couches nucléaire PhD Thesis Université de Caen/Basse-Normandie in French |
| [52] | Corney J F and Drummond P D 2004 Phys. Rev. Lett.93 260401 · doi:10.1103/PhysRevLett.93.260401 |
| [53] | Juillet O 2007 New J. Phys.9 163 · doi:10.1088/1367-2630/9/6/163 |
| [54] | Corboz P R, Kleine A, Assaad F F, McCulloch I P, Schollwöck U and Troyer M 2008 Phys. Rev. B 77 085108 · doi:10.1103/PhysRevB.77.085108 |
| [55] | Buonaura M C and Sorella S 1998 Phys. Rev. B 57 11446 · doi:10.1103/PhysRevB.57.11446 |
| [56] | Kotz S and Nadarajah S 2000 Extreme Value Distributions: Theory and Applications (London: Imperial College Press) · Zbl 0960.62051 · doi:10.1142/p191 |
| [57] | Shi H and Zhang S 2016 Phys. Rev. E 93 033303 · doi:10.1103/PhysRevE.93.033303 |
| [58] | Zhang S, Carlson J and Gubernatis J E 1997 Phys. Rev. B 55 7464 · doi:10.1103/PhysRevB.55.7464 |
| [59] | Purwanto W and Zhang S 2004 Phys. Rev. E 70 056702 · doi:10.1103/PhysRevE.70.056702 |
| [60] | Wick G C 1950 Phys. Rev.80 268 · Zbl 0040.13006 · doi:10.1103/PhysRev.80.268 |
| [61] | Löwdin P-O 1955 Phys. Rev.97 1490 · doi:10.1103/PhysRev.97.1490 |
| [62] | Carlson J, Gandolfi S, Schmidt K E and Zhang S 2011 Phys. Rev. A 84 061602 · doi:10.1103/PhysRevA.84.061602 |
| [63] | Balian R and Brézin E 1969 Il Nuovo Cimento B 64 37 · doi:10.1007/BF02710281 |
| [64] | Gaudin M 1960 Nucl. Phys.15 89 · Zbl 0113.22204 · doi:10.1016/0029-5582(60)90285-6 |
| [65] | Onishi N and Yoshida S 1966 Nucl. Phys.80 367 · doi:10.1016/0029-5582(66)90096-4 |
| [66] | Thouless D J 1960 Nucl. Phys.21 225 · Zbl 0097.43602 · doi:10.1016/0029-5582(60)90048-1 |
| [67] | Cayley A and Forsyth F 1889 The Collected Mathematical Papers of Arthur Cayley (Cambridge: Cambridge University Press) |
| [68] | Bajdich M, Mitas L, Wagner L K and Schmidt K E 2008 Phys. Rev. B 77 115112 · doi:10.1103/PhysRevB.77.115112 |
| [69] | Lieb E H 1960 J. Comb. Theory5 313 · Zbl 0179.03001 · doi:10.1016/S0021-9800(68)80078-X |
| [70] | Wimmer M 2012 ACM Trans. Math. Softw.38 30 · Zbl 1365.65116 · doi:10.1145/2331130.2331138 |
| [71] | Neergard K and Wüst E 1982 Nucl. Phys. A 402 311 · doi:10.1016/0375-9474(83)90501-8 |
| [72] | Schmid K W 2004 Prog. Part. Nucl. Phys.52 565 · doi:10.1016/j.ppnp.2004.02.001 |
| [73] | Robledo L M 2009 Phys. Rev. C 79 021302 · doi:10.1103/PhysRevC.79.021302 |
| [74] | Bertsch G F and Robledo L M 2012 Phys. Rev. Lett.108 042505 · doi:10.1103/PhysRevLett.108.042505 |
| [75] | Hubbard J 1963 Proc. R. Soc. Lond. A 276 238 · doi:10.1098/rspa.1963.0204 |
| [76] | Gutzwiller M C 1963 Phys. Rev. Lett.10 159 · doi:10.1103/PhysRevLett.10.159 |
| [77] | Kanamori J 1963 Prog. Theor. Phys.30 275 · Zbl 0151.46703 · doi:10.1143/PTP.30.275 |
| [78] | Anderson P W 1987 Science235 1196 · doi:10.1126/science.235.4793.1196 |
| [79] | Zhang S, Carlson J and Gubernatis J E 1997 Phys. Rev. Lett.78 4486 · doi:10.1103/PhysRevLett.78.4486 |
| [80] | Guerrero M, Ortiz G and Gubernatis J E 1999 Phys. Rev. B 59 1706 · doi:10.1103/PhysRevB.59.1706 |
| [81] | Moreo A and Scalapino D J 2007 Phys. Rev. Lett.98 216402 · doi:10.1103/PhysRevLett.98.216402 |
| [82] | Shiba H 1972 Prog. Theor. Phys.48 2171 · doi:10.1143/PTP.48.2171 |
| [83] | Shi H, Jiménez-Hoyos C A, Rodríguez-Guzmán R, Scuseria G E and Zhang S 2014 Phys. Rev. B 89 125129 · doi:10.1103/PhysRevB.89.125129 |
| [84] | Eichenberger D and Baeriswyl D 2007 Phys. Rev. B 76 180504 · doi:10.1103/PhysRevB.76.180504 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
