Skip to main content Accessibility help
×
  • Cited by 190
Publisher:
Cambridge University Press
Online publication date:
November 2017
Print publication year:
2017
Online ISBN:
9781316417041

Book description

Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to state-of-the-art quantum Monte Carlo techniques relevant for applications in correlated systems. Providing a clear overview of variational wave functions, and featuring a detailed presentation of stochastic samplings including Markov chains and Langevin dynamics, which are developed into a discussion of Monte Carlo methods. The variational technique is described, from foundations to a detailed description of its algorithms. Further topics discussed include optimisation techniques, real-time dynamics and projection methods, including Green's function, reptation and auxiliary-field Monte Carlo, from basic definitions to advanced algorithms for efficient codes, and the book concludes with recent developments on the continuum space. Quantum Monte Carlo Approaches for Correlated Systems provides an extensive reference for students and researchers working in condensed matter theory or those interested in advanced numerical methods for electronic simulation.

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×

Contents

References
Allen, M. P., and Tildesley, D. J. 1987. Computer Simulation of Liquids. Oxford University Press.
Anderson, H. 1986. Metropolis, Monte Carlo and the MANIAC. Los Alamos Science, 14, 96–108.
Anderson, J. B. 1975. Random walk simulation of the Schrödinger equation: He+. J. Chem. Phys., 63, 1499–1503.
Anderson, J. B. 1976. Quantum chemistry by random walk. J. Chem. Phys., 65, 4121–4127.
Anderson, P. W. 1987. The resonating valence bond state in La2CuO4 and superconductiv- ity. Science, 235, 1196–1198.
Anderson, P. W., Baskaran, G., Zou, Z., and Hsu, T. 1987. Resonating-valence-bond theory of phase transitions and superconductivity in La2CuO4-based compounds. Phys. Rev. Lett., 58, 2790–2793.
Aoki, H., Tsuji, N., Eckstein, M., Kollar, M., Oka, T., and Werner, P. 2014. Non-equilibrium dynamical mean-field theory and its applications. Rev. Mod. Phys., 86, 779–837.
Arovas, D., Schrieffer, J. R., and Wilczek, F. 1984. Fractional statistics and the quantum Hall effect. Phys. Rev. Lett., 53, 722–723.
Bajdich, M., Mitas, L., Drobny, G., Wagner, L. K., and Schmidt, K. E. 2006. Pfaffian pairing wave functions in electronic-structure quantum Monte Carlo simulations. Phys. Rev. Lett., 96, 130201.
Bajdich, M., Mitas, L., Wagner, L. K., and Schmidt, K. E. 2008. Pfaffian pairing and backflow wave functions for electronic-structure quantum Monte Carlo methods. Phys. Rev. B, 77, 115112.
Baldereschi, A. 1973. Mean-value point in the Brillouin zone. Phys. Rev. B, 7, 5212–5215.
Bardeen, J., Cooper, L. N., and Schrieffer, J. R. 1957. Theory of superconductivity. Phys. Rev., 108, 1175–1204.
Baroni, S., and Moroni, S. 1998. Reptation quantum Monte Carlo. arXiv:cond-mat/ 9808213.
Bartlett, R. J. 1981. Many-body perturbation theory and coupled cluster theory for electron correlation in molecules. Ann. Rev. Phys. Chem., 32, 359–401.
Baskaran, G., and Anderson, P. W. 1988. Gauge theory of high-temperature superconduc- tors and strongly correlated Fermi systems. Phys. Rev. B, 37, 580–583.
Bethe, H. 1931. Zur Theorie der metalle. I. eigenwerte und eigenfunktionen der linearen atomkette. Z. Phys., 71, 205–226.
Bouchaud, J. P., Georges, A., and Lhuillier, C. 1988. Pair wave functions for strongly cor- related fermions and their determinantal representation. J. Phys. (Paris), 49, 553–559.
Calandra Buonaura, M., and Sorella, S. 1998. Numerical study of the two-dimensional Heisenberg model using a Green function Monte Carlo technique with a fixed number of walkers. Phys. Rev. B, 57, 11446–11456.
Capello, M., Becca, F., Fabrizio, M., Sorella, S., and Tosatti, E. 2005. Variational description of Mott insulators. Phys. Rev. Lett., 94, 026406.
Capello, M., Becca, F., Yunoki, S., and Sorella, S. 2006. Unconventional metal-insulator transition in two dimensions. Phys. Rev. B, 73, 245116.
Capello, M., Becca, F., Fabrizio, M., and Sorella, S. 2007. Superfluid to Mott-insulator transition in Bose-Hubbard models. Phys. Rev. Lett., 99, 056402.
Capello, M., Becca, F., Fabrizio, M., and Sorella, S. 2008. Mott transition in bosonic systems: insights from the variational approach. Phys. Rev. B, 77, 144517.
Capriotti, L., Becca, F., Parola, A., and Sorella, S. 2001. Resonating valence bond wave functions for strongly frustrated spin systems. Phys. Rev. Lett., 87, 097201.
Carleo, G., Becca, F., Schiro, M., and Fabrizio, M. 2012. Localization and glassy dynamics of many-body quantum system. Sci. Rep., 2, 243.
Carleo, G., Becca, F., Sanchez-Palencia, L., Sorella, S., and Fabrizio, M. 2014. Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids. Phys. Rev. A, 89, 031602.
Casula, M., Filippi, C., and Sorella, S. 2005. Diffusion Monte Carlo method with lattice regularization. Phys. Rev. Lett., 95, 100201.
Ceperley, D., Chester, G. V., and Kalos, M.H. 1977. Monte Carlo simulation of a many- fermion study. Phys. Rev. B, 16, 3081–3099.
Ceperley, D. M. 1991. Fermion nodes. J. Stat. Phys., 63, 1237–1267.
Ceperley, D. M., and Alder, B. J. 1980. Ground state of the electron gas by a stochastic method. Phys. Rev. Lett., 45, 566–569.
Corboz, P., Rice, T. M., and Troyer, M. 2014. Competing states in the t-J model: uniform d-wave state versus stripe state. Phys. Rev. Lett., 113, 046402.
Daley, A. J., Kollath, C., Schollwöck, U., and Vidal, G. 2004. Time-dependent density- matrix renormalization-group using adaptive effective Hilbert spaces. J. Stat. Mech.: Theor. Exp., P04005.
Dirac, P. A. M. 1930. Note on exchange phenomena in the Thomas atom. Math. Proc. Cambridge Philos. Soc., 26, 376–385.
Dongarra, J., and Sullivan, F. 2000. Guest editors' introduction: the top 10 algorithms. Comput. Sci Eng., 2, 22–23.
Dovesi, R., Orlando, R., Erba, A., Zicovich-Wilson, C. M., Civalleri, B., Casassa, S., Maschio, L., Ferrabone, M., De La Pierre, M., D'Arco, P., Noel, Y., Causa`, M., Rerat, M., and Kirtman, B. 2014. CRYSTAL14: a program for the ab initio investigation of crystalline solids. Int. J. Quantum Chem., 114, 1287–1317.
Eichenberger, D., and Baeriswyl, D. 2007. Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: a variational study. Phys. Rev. B, 76, 180504.
Eisert, J., Cramer, M., and Plenio, M. B. 2010. Area laws for the entanglement entropy. Rev. Mod. Phys., 82, 277–306.
Faddeev, L. D., and Takhtajan, L. A. 1981. What is the spin of a spin wave? Phys. Lett. A, 85, 375–377.
Fahy, S., and Hamann, D. R. 1991. Diffusive behavior of states in the Hubbard-Stratonovich transformation. Phys. Rev. B, 43, 765–779.
Fano, G., Ortolani, F., and Colombo, E. 1986. Configuration-interaction calculations on the fractional quantum Hall effect. Phys. Rev. B, 34, 2670–2680.
Fazekas, P. 1999. Lecture Notes on Electron Correlation and Magnetism. World Scientifi.
Fazekas, P., and Anderson, P. W. 1974. On the ground state properties of the anisotropic triangular antiferromagnet. Phil. Mag., 30, 423–440.
Ferrenberg, A. M., Landau, D. P., and Wong, Y. J. 1992. Monte Carlo simulations: Hidden errors from “good” random number generators. Phys. Rev. Lett., 69, 3382–3384.
Fetter, A. L., and Walecka, J. D. 2003. Quantum Theory of Many-Particle Systems. Dover Publications Inc.
Feynman, R. P. 1954. Atomic theory of the two-fluid model of liquid Helium. Phys. Rev., 94, 262–277.
Feynman, R. P., and Cohen, M. 1956. Energy spectrum of the excitations in liquid Helium. Phys. Rev., 102, 1189–1204.
Filippi, C., and Umrigar, C. 1996. Multiconfiguration wave functions for quantum Monte Carlo calculations of first-row diatomic molecules. J. Chem. Phys., 105, 213–226.
Foulkes, W. M. C., Mitas, L., Needs, R. J., and Rajagopal, G. 2001. Quantum Monte Carlo simulations of solids. Rev. Mod. Phys., 73, 33–83.
Gnedenko, B. V. 2014. The Theory of Probability. Martino Fine Books.
Gnedenko, B. V., and Kolmogorov, A. N. 1954. Limit Distributions for Sums of Independent Random Variables. Addison-Wesley.
Gros, C. 1988. Superconductivity in correlated wave functions. Phys. Rev. B, 38, 931–934.
Gros, C. 1989. Physics of projected wave functions. Ann. Phys., 189, 53–88.
Gros, C., Joynt, R., and Rice, T. M. 1987. Antiferromagnetic correlations in almost- localized Fermi liquids. Phys. Rev. B, 36, 381–393.
Gubernatis, J., Kawashima, N., and Werner, P. 2016. Quantum Monte Carlo methods: algorithms for lattice models. Cambridge University Press.
Gutzwiller, M. C. 1963. Effect of correlation on the ferromagnetism of transition metals. Phys. Rev. Lett., 10, 159–162.
Haldane, F. D. M. 1983. Fractional quantization of the Hall effect: a hierarchy of incompressible quantum fluid states. Phys. Rev. Lett., 51, 605–608.
Haldane, F. D. M. 1988. Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-1/2 antiferromagnetic Heisenberg chain with 1/r2 exchange. Phys. Rev. Lett., 60, 635–638.
Haldane, F. D. M. 1991. “Spinon gas” description of the S = 1/2 Heisenberg chain with inverse-square exchange: exact spectrum and thermodynamics. Phys. Rev. Lett., 66, 1529–1532.
Haldane, F. D. M., and Rezayi, E. H. 1985. Periodic Laughlin-Jastrow wave functions for the fractional quantized Hall effect. Phys. Rev. B, 60, 2529–2531.
Harju, A., Barbiellini, B., Siljamaki, S., Nieminen, R. M., and Ortiz, G. 1997. Stochastic gradient approximation: an efficient method to optimize many-body wave functions. Phys. Rev. Lett., 79, 1173–1177.
Hastings, W. K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97–109.
Heitler, W., and London, F. 1927. Wechselwirkung neutraler atome und homöopolare bindung nach der quantenmechanik. Z. Phys., 44, 455–472.
Hirsch, J. E. 1985. Two-dimensional Hubbard model: numerical simulation study. Phys. Rev. B, 31, 4403–4419.
Hu, W.-J., Becca, F., and Sorella, S. 2012. Absence of static stripes in the two-dimensional t-J model determined using an accurate and systematic quantum Monte Carlo approach. Phys. Rev. B, 85, 081110.
Hubbard, J. 1959. Calculation of partition functions. Phys. Rev. Lett., 3, 77–78.
Hubbard, J. 1963. Electron correlations in narrow energy bands. Proc. Royal Soc. of London, 276, 238–257.
Ido, K., Ohgoe, T., and Imada, M. 2015. Time-dependent many-variable variational Monte Carlo method for non-equilibrium strongly correlated electron systems. Phys. Rev. B, 92, 245106.
Imada, M., Fujimori, A., and Tokura, Y. 1998. Metal-insulator transitions. Rev. Mod. Phys., 70, 1039–1263.
Iqbal, Y., Becca, F., and Poilblanc, D. 2011. Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet. Phys. Rev. B, 84, 020407.
Jain, J. K. 2012. Composite Fermions. Cambridge University Press.
Jastrow, R. 1955. Many-body problem with strong forces. Phys. Rev., 98, 1479–1484.
Kalos, M. H., Levesque, D., and Verlet, L. 1974. Helium at zero temperature with hard-sphere and other forces. Phys. Rev. A, 9, 2178–2195.
Kanamori, J. 1963. Electron correlation and ferromagnetism of transition metals. Prog. Theor. Phys., 30, 275–289.
Kaneko, R., Tocchio, L. F., Valenti, R., Becca, F., and Gros, C. 2016. Spontaneous symmetry breaking in correlated wave functions. Phys. Rev. B, 93, 125127.
Kim, J., Esler, K. P., McMinis, J., Morales, M. A., Clark, B. K., Shulenburger, L., and D. M., Ceperley. 2012. Hybrid algorithms in quantum Monte Carlo. J. Phys.: Conf. Ser., 402, 012008.
Kivelson, S. A., Rokhsar, D. S., and Sethna, J. P. 1987. Topology of the resonating valence-bond state: solitons and high-Tc superconductivity. Phys. Rev. B, 35, 8865– 8868.
Knuth, D. 1997. The Art of Computer Programming. Addison-Wesley.
Krauth, W. 2006. Statistical Mechanics: Algorithms and Computations. Oxford University Press.
Krauth, W., Caffarel, M., and Bouchaud, J. 1992. Gutzwiller wave function for a model of strongly interacting bosons. Phys. Rev. B, 45, 3137–3140.
Kwon, Y., Ceperley, D. M., and Martin, R. M. 1993. Effects of three-body and backflow correlations in the two-dimensional electron gas. Phys. Rev. B, 48, 12037–12046.
Kwon, Y., Ceperley, D. M., and Martin, R. M. 1998. Effects of backflow correlation in the three-dimensional electron gas: quantum Monte Carlo study. Phys. Rev. B, 58, 6800–6806.
Laughlin, R. B. 1983. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett., 50, 1395–1398.
Lee, P. A., Nagaosa, N., and Wen, X.-G. 2006. Doping a Mott insulator: physics of high- temperature superconductivity. Rev. Mod. Phys., 78, 17–85.
Liang, S., Doucot, B., and Anderson, P. W. 1988. Some new variational resonating-valence- bond-type wave functions for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice. Phys. Rev. Lett., 61, 365–368.
Lieb, E. H., and Wu, F. Y. 1968. Absence of Mott transition in an exact solution of the short-range, one-band model in one dimension. Phys. Rev. Lett., 20, 1445–1448.
Lin, C., Zong, F. H., and Ceperley, D. M. 2001. Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms. Phys. Rev. E, 64, 016702.
Loh, E. Y., Gubernatis, J. E., Scalettar, R. T., White, S. R., Scalapino, D. J., and Sugar, R. L. 1990. Sign problem in the numerical simulation of many-electron systems. Phys. Rev. B, 41, 9301–9307.
Marchi, M., Azadi, S., Casula, M., and Sorella, S. 2009. Resonating valence bond wave function with molecular orbitals: Application to first-row molecules. J. Chem. Phys., 131, 154116.
Marshall, W. 1955. Antiferromagnetism. Proc. R. Soc. London Ser., A 232, 48–68.
Martin, R. M. 2004. Electronic Structure: Basic Theory and Practical Methods. Cambridge University Press.
Martin, R.M., Reining, L., and Ceperley, D.M. 2016. Interacting Electrons: Theory and Computational Approaches. Cambridge University Press.
Mazzola, G., and Sorella, S. 2017. Accelerating ab initio molecular dynamics and probing the weak dispersive forces in dense liquid Hydrogen. Phys. Rev. Lett., 118, 015703.
McMillan, W. L. 1965. Ground State of Liquid He4. Phys. Rev., 138, A442–A451.
Metropolis, N. 1987. The beginning of the Monte Carlo method. Los Alamos Science, 15, 125–130.
Metropolis, N., and Ulam, S. 1949. The Monte Carlo method. J. Am. Stat. Ass., 44, 335–341.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E. 1957. Equations of state calculations by fast computing machines. J. Chem. Phys., 21, 1087–1092.
Meyer, C. D. 2000. Matrix Analysis and Applied Linear Algebra. SIAM.
Moore, G., and Read, N. 1991. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B, 360, 362–396.
Moroni, S., and Baroni, S. 1999. Reptation quantum Monte Carlo: A method for unbi- ased ground-state averages and imaginary-time correlations. Phys. Rev. Lett., 82, 4745–4748.
Moskowitz, J. W., Schmidt, K. E., Lee, M. A., and Kalos, M. H. 1982. A new look at correlation energy in atomic and molecular systems. II: the application of the Green's function Monte Carlo method to LiH. J. Chem. Phys., 77, 349–355.
Mott, N. F. 1949. The basis of the electron theory of metals, with special reference to the transition metals. Proc. Phys. Soc. (London), 62, 416–422.
Mott, N. F. 1990. Metal-Insulator Transitions. Taylor and Francis.
Nagaoka, Y. 1966. Ferromagnetism in a narrow, almost half-filled s band. Phys. Rev., 147, 392–405.
Needs, R. J., Towler, M. D., Drummond, N. D., and Lopez Rıos, P. 2010. Continuum variational and diffusion quantum Monte Carlo calculations. J. Phys.: Condens. Matter, 22, 023201.
Nelson, E. 1966. Derivation of the Schrödinger equation from Newtonian mechanics. Phys. Rev., 150, 1079–1085.
Neuscamman, E. 2012. Size consistency error in the antisymmetric geminal power wave function can be completely removed. Phys. Rev. Lett., 109, 203001.
Neuscamman, E., Umrigar, C. J., and Chan, G.K.-L. 2012. Optimizing large parameter sets in variational quantum Monte Carlo. Phys. Rev. B, 85, 045103.
Nightingale, M. P., and Melik-Alaverdian, V. 2001. Optimization of ground- and excited- state wave functions and van der Waals clusters. Phys. Rev. Lett., 87, 043401.
Norris, J. R. 1997. Markov Chains. Cambridge Series in Statistical and Probabilistic Mathematics.
Nozieres, P. 1964. Theory of Interacting Fermi Systems. New York: W.A. Benjamin.
Ortiz, G., Ceperley, D. M., and Martin, R. M. 1993. New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field. Phys. Rev. Lett., 71, 2777–2780.
Oshikawa, M., and Senthil, T. 2006. Fractionalization, topological order, and quasiparticle statistics. Phys. Rev. Lett., 96, 060601.
Pandharipande, V. R., and Itoh, N. 1973. Effective mass of 3He in liquid 4He. Phys. Rev. A, 8, 2564–2566.
Parisi, G. 1984. Prolegomena to any future computer evaluation of the QCD mass spectrum. Pages 531–541 of: Progress in Gauge Field Theory. NATO ASI Series, vol. 115. Springe.
Parisi, G., and Wu, Y.-S. 1981. Perturbation theory without gauge fixing. Sci. Sinica, 24, 483–496.
Pauling, L. 1960. The Nature of the Chemical Bond. Cornell University Press.
Pierleoni, C., and Ceperley, D. M. 2005. Computational methods in coupled electronion Monte Carlo simulations. ChemPhysChem, 6, 1872–1878.
Pitaevskii, L., and Stringari, S. 1991. Uncertainly principle, quantum fluctuations, and broken symmetries. J. Low Temp. Phys., 85, 377–388.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. 2007. Numerical Recipes 3rd edition: The Art of Scientific Computing. Cambridge University Press.
Read, N., and Chakraborty, B. 1989. Statistics of the excitations of the resonating-valence- bond state. Phys. Rev. B, 40, 7133–7140.
Read, N., and Rezayi, E. 1999. Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level. Phys. Rev. B, 59, 8084–8092.
Reger, J. D., and Young, A. P. 1988. Monte Carlo simulations of the spin-1/2 Heisenberg antiferromagnet on a square lattice. Phys. Rev. B, 37, 5978–5981.
Reynolds, P. J., Ceperley, D. M., Alder, B. J., and Lester, Jr. 1982. Fixednode quantum Monte Carlo for molecules. J. Chem. Phys., 77, 5593–5603.
Ring, P., and Schuck, P. 2004. The Nuclear Many-body Problem. Springer-Verlag. Rokhsar, D. S., and Kotliar, B. G. 1991. Gutzwiller projection for bosons. Phys. Rev. B, 44, 10328–10332.
Schmidt, K. E., and Pandharipande, V. R. 1979. New variational wave function for liquid 3He. Phys. Rev. B, 19, 2504–2519.
Schollwöck, U. 2005. The density-matrix renormalization group. Rev. Mod. Phys., 77, 259–315.
Schollwöck, U. 2011. The density-matrix renormalization group in the age of matrix product states. Ann. Phys., 326, 96–192.
Schrieffer, J. R. 1964. Theory of Superconductivity. New York: W.A. Benjamin.
Senthil, T., and Fisher, M. P. A. 2000. Z2 gauge theory of electron fractionalization in strongly correlated systems. Phys. Rev. B, 62, 7850–7881.
Shastry, B. S. 1988. Exact solution of an S = 1/2 Heisenberg antiferromagnetic chain with long-ranged interactions. Phys. Rev. Lett., 60, 639–642.
Slater, J. C. 1930. The electronic structure of metals. Rev. Mod. Phys., 6, 209–280.
Sorella, S. 1998. Green function Monte Carlo with stochastic reconfiguration. Phys. Rev. Lett., 80, 4558–4561.
Sorella, S. 2001. Generalized Lanczos algorithm for variational quantum Monte Carlo. Phys. Rev. B, 64, 024512.
Sorella, S. 2002. Effective Hamiltonian approach for strongly correlated lattice models. arXiv:cond-mat/0201388.
Sorella, S. 2005. Wave function optimization in the variational Monte Carlo method. Phys. Rev. B, 71, 241103.
Sorella, S., Baroni, S., Car, R., and Parrinello, M. 1989. A novel technique for the simulation of interacting fermion systems. Europhys. Lett., 8, 663–668.
Sorella, S., Martins, G. B., Becca, F., Gazza, C., Capriotti, L., Parola, A., and Dagotto, E. 2002. Superconductivity in the two-dimensional t-J model. Phys. Rev. Lett., 88, 117002.
Sorella, S., Casula, M., and Rocca, D. 2007. Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods. J. Chem. Phys., 127, 014105.
Sorella, S., Devaux, N., Dagrada, M., Mazzola, G., and Casula, M. 2015. Geminal embedding scheme for optimal atomic basis set construction in correlated calculations. J. Chem. Phys., 143, 244112.
Stewart, G. R. 1984. Heavy-fermion systems. Rev. Mod. Phys., 56, 755–787.
Stratonovich, R. L. 1957. A method for the computation of quantum distribution functions. Doklady Akad. Nauk S.S.S.R., 115, 1097–1100.
Sutherland, B. 1971. Exact results for a quantum many-body problem in one dimension. Phys. Rev. A, 4, 2019–2021.
Sutherland, B. 1975. Model for a multicomponent quantum system. Phys. Rev. B, 12, 3795–3805.
Suzuki, M. 1976a. Generalized Trotter's formula and systematic approximants of expo- nential operators and inner derivations with applications to many-body problems. Commun. Math. Phys., 51, 183–190.
Suzuki, M. 1976b. Relationship between d-dimensional quantal spin systems and (d + 1)- dimensional Ising systems. Prog. Theor. Phys., 56, 1454–1469.
Szabo, A., and Ostlund, N. S. 1996. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover Publications Inc.
Tasaki, H. 1998. From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond. Prog. Theor. Phys., 99, 489–548.
ten Haaf, D. F. B., van Bemmel, H. J. M., van Leeuwen, J. M. J., van Saarloos, W., and Ceperley, D. M. 1995. Proof of upper bound in fixed-node Monte Carlo for lattice fermions. Phys. Rev. B, 51, 13039–13045.
Tocchio, L. F., Becca, F., Parola, A., and Sorella, S. 2008. Role of backflow correlations for the nonmagnetic phase of the t-tl Hubbard model. Phys. Rev. B, 78, 041101.
Tocchio, L. F., Becca, F., and Gros, C. 2011. Backflow correlations in the Hubbard model: An efficient tool for the study of the metal-insulator transition and the large-U limit. Phys. Rev. B, 83, 195138.
Toulouse, J., and Umrigar, C. J. 2007. Optimization of quantum Monte Carlo wave functions by energy minimization. J. Chem. Phys., 126, 084102.
Trivedi, N., and Ceperley, D. M. 1989. Green-function Monte Carlo study of quantum antiferromagnets. Phys. Rev. B, 40, 2737–2740.
Trivedi, N., and Ceperley, D. M. 1990. Ground-state correlations of quantum antiferromag- nets: a Green-function Monte Carlo study. Phys. Rev. B, 41, 4552–4569.
Trotter, H. F. 1959. On the product of semi-groups of operators. Proc. Am. Math. Soc., 10, 545–551.
Tuckerman, M. E. 2010. Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press.
Umrigar, C. J., and Filippi, C. 2005. Energy and variance optimization of many-body wave functions. Phys. Rev. Lett., 94, 150201.
Umrigar, C. J., Wilson, K. G., and Wilkins, J. W. 1988. Optimized trial wave functions for quantum Monte Carlo calculations. Phys. Rev. Lett., 60, 1719–1722.
Umrigar, C. J., Nightingale, M. P., and Runge, K. J. 1993. A diffusion Monte Carlo algorithm with very small timestep errors. J. Chem. Phys., 99, 2865–2890.
Umrigar, C. J., Toulouse, J., Filippi, C., Sorella, S., and Hennig, R. G. 2007. Alleviation of the fermion-sign problem by optimization of many-body wave functions. Phys. Rev. Lett., 98, 110201.
Wagner, L. K., Bajdich, M., and Mitas, L. 2009. QWalk: A quantum Monte Carlo program for electronic structure. J. Comp. Phys., 228, 3390–3404.
Wen, X.-G. 1991. Topological orders and Chern-Simons theory in strongly correlated quantum liquid. Int. J. Mod. Phys. B, 5, 1641–1648.
Wen, X.-G., and Niu, Q. 1990. Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces. Phys. Rev. B, 41, 9377–9396.
White, S. R. 1992. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett., 69, 2863–2866.
White, S. R, and Feiguin, A. 2004. Real-time evolution using the density matrix renormal- ization group. Phys. Rev. Lett., 93, 076401.
White, S. R., and Scalapino, D.J. 1998. Density matrix renormalization group study of the striped phase in the 2D t-J model. Phys. Rev. Lett., 80, 1272–1275.
Wigner, E., and Seitz, F. 1934. On the constitution of metallic Sodium. II. Phys. Rev., 46, 509–524.
Yokoyama, H., and Shiba, H. 1987a. Variational Monte Carlo studies of Hubbard model. I. J. Phys. Soc. Jpn., 56, 1490–1506.
Yokoyama, H., and Shiba, H. 1987b. Variational Monte Carlo studies of Hubbard model. II. J. Phys. Soc. Jpn., 56, 3582–3592.
Yokoyama, H., and Shiba, H. 1990. Variational Monte Carlo studies of Hubbard model. III. Intersite correlation effects. J. Phys. Soc. Jpn., 59, 3669–3686.
Young, P. 2012. Everything you wanted to know about data analysis and fitting but were afraid to ask. arXiv:1210.3781.
Zhang, F. C., and Rice, T. M. 1988. Effective Hamiltonian for the superconducting Cu oxides. Phys. Rev. B, 37, 3759–3761.
Zhang, S., Carlson, J., and Gubernatis, J. E. 1995. Constrained path quantum Monte Carlo method for fermion ground states. Phys. Rev. Lett., 74, 3652–3655.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.