References
Published online by Cambridge University Press: 17 November 2017
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Quantum Monte Carlo Approaches for Correlated Systems , pp. 264 - 271Publisher: Cambridge University PressPrint publication year: 2017
References
, and 1987. Computer Simulation of Liquids. Oxford University Press.
1975. Random walk simulation of the Schrödinger equation: He+. J. Chem. Phys., 63, 1499–1503.Google Scholar
1987. The resonating valence bond state in La2CuO4 and superconductiv- ity. Science, 235, 1196–1198.Google Scholar
, , , and 1987. Resonating-valence-bond theory of phase transitions and superconductivity in La2CuO4-based compounds. Phys. Rev. Lett., 58, 2790–2793.Google Scholar
, , , , , and 2014. Non-equilibrium dynamical mean-field theory and its applications. Rev. Mod. Phys., 86, 779–837.Google Scholar
, , and 1984. Fractional statistics and the quantum Hall effect. Phys. Rev. Lett., 53, 722–723.Google Scholar
, , , , and 2006. Pfaffian pairing wave functions in electronic-structure quantum Monte Carlo simulations. Phys. Rev. Lett., 96, 130201.Google Scholar
, , , and 2008. Pfaffian pairing and backflow wave functions for electronic-structure quantum Monte Carlo methods. Phys. Rev. B, 77, 115112.Google Scholar
, and 1998. Reptation quantum Monte Carlo. arXiv:cond-mat/ 9808213.
1981. Many-body perturbation theory and coupled cluster theory for electron correlation in molecules. Ann. Rev. Phys. Chem., 32, 359–401.Google Scholar
, and 1988. Gauge theory of high-temperature superconduc- tors and strongly correlated Fermi systems. Phys. Rev. B, 37, 580–583.Google Scholar
1931. Zur Theorie der metalle. I. eigenwerte und eigenfunktionen der linearen atomkette. Z. Phys., 71, 205–226.Google Scholar
, , and 1988. Pair wave functions for strongly cor- related fermions and their determinantal representation. J. Phys. (Paris), 49, 553–559.Google Scholar
, and 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.Google Scholar
, , , , and 2005. Variational description of Mott insulators. Phys. Rev. Lett., 94, 026406.Google Scholar
, , , and 2006. Unconventional metal-insulator transition in two dimensions. Phys. Rev. B, 73, 245116.Google Scholar
, , , and 2007. Superfluid to Mott-insulator transition in Bose-Hubbard models. Phys. Rev. Lett., 99, 056402.Google Scholar
, , , and 2008. Mott transition in bosonic systems: insights from the variational approach. Phys. Rev. B, 77, 144517.Google Scholar
, , , and 2001. Resonating valence bond wave functions for strongly frustrated spin systems. Phys. Rev. Lett., 87, 097201.Google Scholar
, , , and 2012. Localization and glassy dynamics of many-body quantum system. Sci. Rep., 2, 243.Google Scholar
, , Sanchez-Palencia, L., , and 2014. Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids. Phys. Rev. A, 89, 031602.Google Scholar
, , and 2005. Diffusion Monte Carlo method with lattice regularization. Phys. Rev. Lett., 95, 100201.Google Scholar
, , and H. 1977. Monte Carlo simulation of a many- fermion study. Phys. Rev. B, 16, 3081–3099.Google Scholar
, and 1980. Ground state of the electron gas by a stochastic method. Phys. Rev. Lett., 45, 566–569.Google Scholar
, , and 2014. Competing states in the t-J model: uniform d-wave state versus stripe state. Phys. Rev. Lett., 113, 046402.Google Scholar
, , , and 2004. Time-dependent density- matrix renormalization-group using adaptive effective Hilbert spaces. J. Stat. Mech.: Theor. Exp., P04005.
M. 1930. Note on exchange phenomena in the Thomas atom. Math. Proc. Cambridge Philos. Soc., 26, 376–385.Google Scholar
, and 2000. Guest editors' introduction: the top 10 algorithms. Comput. Sci Eng., 2, 22–23.Google Scholar
, , , Zicovich-Wilson, C. M., , , , , De La , D'Arco, P., Noel, Y., , Rerat, M., and 2014. CRYSTAL14: a program for the ab initio investigation of crystalline solids. Int. J. Quantum Chem., 114, 1287–1317.Google Scholar
, and 2007. Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: a variational study. Phys. Rev. B, 76, 180504.Google Scholar
, and 1991. Diffusive behavior of states in the Hubbard-Stratonovich transformation. Phys. Rev. B, 43, 765–779.Google Scholar
, , and 1986. Configuration-interaction calculations on the fractional quantum Hall effect. Phys. Rev. B, 34, 2670–2680.Google Scholar
1999. Lecture Notes on Electron Correlation and Magnetism. World Scientifi.
, and 1974. On the ground state properties of the anisotropic triangular antiferromagnet. Phil. Mag., 30, 423–440.Google Scholar
, , and 1992. Monte Carlo simulations: Hidden errors from “good” random number generators. Phys. Rev. Lett., 69, 3382–3384.Google Scholar
, and 2003. Quantum Theory of Many-Particle Systems. Dover Publications Inc.
, and 1956. Energy spectrum of the excitations in liquid Helium. Phys. Rev., 102, 1189–1204.Google Scholar
, and 1996. Multiconfiguration wave functions for quantum Monte Carlo calculations of first-row diatomic molecules. J. Chem. Phys., 105, 213–226.Google Scholar
C., , , and 2001. Quantum Monte Carlo simulations of solids. Rev. Mod. Phys., 73, 33–83.Google Scholar
2014. The Theory of Probability. Martino Fine Books.
, and 1954. Limit Distributions for Sums of Independent Random Variables. Addison-Wesley.
, , and 1987. Antiferromagnetic correlations in almost- localized Fermi liquids. Phys. Rev. B, 36, 381–393.Google Scholar
, , and 2016. Quantum Monte Carlo methods: algorithms for lattice models. Cambridge University Press.
1963. Effect of correlation on the ferromagnetism of transition metals. Phys. Rev. Lett., 10, 159–162.Google Scholar
1983. Fractional quantization of the Hall effect: a hierarchy of incompressible quantum fluid states. Phys. Rev. Lett., 51, 605–608.Google Scholar
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.Google Scholar
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.Google Scholar
, and 1985. Periodic Laughlin-Jastrow wave functions for the fractional quantized Hall effect. Phys. Rev. B, 60, 2529–2531.Google Scholar
, , Siljamaki, S., , and 1997. Stochastic gradient approximation: an efficient method to optimize many-body wave functions. Phys. Rev. Lett., 79, 1173–1177.Google Scholar
1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97–109.Google Scholar
, and 1927. Wechselwirkung neutraler atome und homöopolare bindung nach der quantenmechanik. Z. Phys., 44, 455–472.Google Scholar
1985. Two-dimensional Hubbard model: numerical simulation study. Phys. Rev. B, 31, 4403–4419.Google Scholar
, , and 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.Google Scholar
1963. Electron correlations in narrow energy bands. Proc. Royal Soc. of London, 276, 238–257.Google Scholar
, , and 2015. Time-dependent many-variable variational Monte Carlo method for non-equilibrium strongly correlated electron systems. Phys. Rev. B, 92, 245106.Google Scholar
, , and 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.Google Scholar
2012. Composite Fermions. Cambridge University Press.
, , and 1974. Helium at zero temperature with hard-sphere and other forces. Phys. Rev. A, 9, 2178–2195.Google Scholar
1963. Electron correlation and ferromagnetism of transition metals. Prog. Theor. Phys., 30, 275–289.Google Scholar
, , , , and 2016. Spontaneous symmetry breaking in correlated wave functions. Phys. Rev. B, 93, 125127.Google Scholar
, , , , , , and D. M., Ceperley. 2012. Hybrid algorithms in quantum Monte Carlo. J. Phys.: Conf. Ser., 402, 012008.Google Scholar
, , and 1987. Topology of the resonating valence-bond state: solitons and high-Tc superconductivity. Phys. Rev. B, 35, 8865– 8868.Google Scholar
1997. The Art of Computer Programming. Addison-Wesley.
2006. Statistical Mechanics: Algorithms and Computations. Oxford University Press.
, , and 1992. Gutzwiller wave function for a model of strongly interacting bosons. Phys. Rev. B, 45, 3137–3140.Google Scholar
, , and 1993. Effects of three-body and backflow correlations in the two-dimensional electron gas. Phys. Rev. B, 48, 12037–12046.Google Scholar
, , and 1998. Effects of backflow correlation in the three-dimensional electron gas: quantum Monte Carlo study. Phys. Rev. B, 58, 6800–6806.Google Scholar
1983. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett., 50, 1395–1398.Google Scholar
, , and -G. 2006. Doping a Mott insulator: physics of high- temperature superconductivity. Rev. Mod. Phys., 78, 17–85.Google Scholar
, , and 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.Google Scholar
, and 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.Google Scholar
, , and 2001. Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms. Phys. Rev. E, 64, 016702.Google Scholar
, , , , , and 1990. Sign problem in the numerical simulation of many-electron systems. Phys. Rev. B, 41, 9301–9307.Google Scholar
, , , and 2009. Resonating valence bond wave function with molecular orbitals: Application to first-row molecules. J. Chem. Phys., 131, 154116.Google Scholar
2004. Electronic Structure: Basic Theory and Practical Methods. Cambridge University Press.
M., , and M. 2016. Interacting Electrons: Theory and Computational Approaches. Cambridge University Press.
, and 2017. Accelerating ab initio molecular dynamics and probing the weak dispersive forces in dense liquid Hydrogen. Phys. Rev. Lett., 118, 015703.Google Scholar
, , , , and 1957. Equations of state calculations by fast computing machines. J. Chem. Phys., 21, 1087–1092.Google Scholar
2000. Matrix Analysis and Applied Linear Algebra. SIAM.
, and 1991. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B, 360, 362–396.Google Scholar
, and 1999. Reptation quantum Monte Carlo: A method for unbi- ased ground-state averages and imaginary-time correlations. Phys. Rev. Lett., 82, 4745–4748.Google Scholar
, , , and 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.Google Scholar
1949. The basis of the electron theory of metals, with special reference to the transition metals. Proc. Phys. Soc. (London), 62, 416–422.Google Scholar
1990. Metal-Insulator Transitions. Taylor and Francis.
1966. Ferromagnetism in a narrow, almost half-filled s band. Phys. Rev., 147, 392–405.Google Scholar
, , , and Lopez Rıos, P. 2010. Continuum variational and diffusion quantum Monte Carlo calculations. J. Phys.: Condens. Matter, 22, 023201.Google Scholar
1966. Derivation of the Schrödinger equation from Newtonian mechanics. Phys. Rev., 150, 1079–1085.Google Scholar
2012. Size consistency error in the antisymmetric geminal power wave function can be completely removed. Phys. Rev. Lett., 109, 203001.Google Scholar
, , and K.-L. 2012. Optimizing large parameter sets in variational quantum Monte Carlo. Phys. Rev. B, 85, 045103.Google Scholar
, and Melik-Alaverdian, V. 2001. Optimization of ground- and excited- state wave functions and van der Waals clusters. Phys. Rev. Lett., 87, 043401.Google Scholar
1997. Markov Chains. Cambridge Series in Statistical and Probabilistic Mathematics.
1964. Theory of Interacting Fermi Systems. New York: W.A. Benjamin.
, , and 1993. New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field. Phys. Rev. Lett., 71, 2777–2780.Google Scholar
, and 2006. Fractionalization, topological order, and quasiparticle statistics. Phys. Rev. Lett., 96, 060601.Google Scholar
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.
1960. The Nature of the Chemical Bond. Cornell University Press.
, and 2005. Computational methods in coupled electronion Monte Carlo simulations. ChemPhysChem, 6, 1872–1878.Google Scholar
, and 1991. Uncertainly principle, quantum fluctuations, and broken symmetries. J. Low Temp. Phys., 85, 377–388.Google Scholar
, , , and 2007. Numerical Recipes 3rd edition: The Art of Scientific Computing. Cambridge University Press.
, and 1989. Statistics of the excitations of the resonating-valence- bond state. Phys. Rev. B, 40, 7133–7140.Google Scholar
, and 1999. Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level. Phys. Rev. B, 59, 8084–8092.Google Scholar
, and 1988. Monte Carlo simulations of the spin-1/2 Heisenberg antiferromagnet on a square lattice. Phys. Rev. B, 37, 5978–5981.Google Scholar
, , , and Lester, Jr. 1982. Fixednode quantum Monte Carlo for molecules. J. Chem. Phys., 77, 5593–5603.Google Scholar
, and 2004. The Nuclear Many-body Problem. Springer-Verlag. , and 1991. Gutzwiller projection for bosons. Phys. Rev. B, 44, 10328–10332.Google Scholar
, and 1979. New variational wave function for liquid 3He. Phys. Rev. B, 19, 2504–2519.Google Scholar
2011. The density-matrix renormalization group in the age of matrix product states. Ann. Phys., 326, 96–192.Google Scholar
1964. Theory of Superconductivity. New York: W.A. Benjamin.
, and A. 2000. Z2 gauge theory of electron fractionalization in strongly correlated systems. Phys. Rev. B, 62, 7850–7881.Google Scholar
1988. Exact solution of an S = 1/2 Heisenberg antiferromagnetic chain with long-ranged interactions. Phys. Rev. Lett., 60, 639–642.Google Scholar
1998. Green function Monte Carlo with stochastic reconfiguration. Phys. Rev. Lett., 80, 4558–4561.Google Scholar
2001. Generalized Lanczos algorithm for variational quantum Monte Carlo. Phys. Rev. B, 64, 024512.Google Scholar
2002. Effective Hamiltonian approach for strongly correlated lattice models. arXiv:cond-mat/0201388.
2005. Wave function optimization in the variational Monte Carlo method. Phys. Rev. B, 71, 241103.Google Scholar
, , , and 1989. A novel technique for the simulation of interacting fermion systems. Europhys. Lett., 8, 663–668.Google Scholar
, , , , , , and 2002. Superconductivity in the two-dimensional t-J model. Phys. Rev. Lett., 88, 117002.Google Scholar
, , and 2007. Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods. J. Chem. Phys., 127, 014105.Google Scholar
, , , , and 2015. Geminal embedding scheme for optimal atomic basis set construction in correlated calculations. J. Chem. Phys., 143, 244112.Google Scholar
1957. A method for the computation of quantum distribution functions. Doklady Akad. Nauk S.S.S.R., 115, 1097–1100.Google Scholar
1971. Exact results for a quantum many-body problem in one dimension. Phys. Rev. A, 4, 2019–2021.Google Scholar
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.Google Scholar
1976b. Relationship between d-dimensional quantal spin systems and (d + 1)- dimensional Ising systems. Prog. Theor. Phys., 56, 1454–1469.Google Scholar
, and 1996. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover Publications Inc.
1998. From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond. Prog. Theor. Phys., 99, 489–548.Google Scholar
, van M., van J., van , and 1995. Proof of upper bound in fixed-node Monte Carlo for lattice fermions. Phys. Rev. B, 51, 13039–13045.Google Scholar
, , , and 2008. Role of backflow correlations for the nonmagnetic phase of the t-tl Hubbard model. Phys. Rev. B, 78, 041101.Google Scholar
, , and 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.Google Scholar
, and 2007. Optimization of quantum Monte Carlo wave functions by energy minimization. J. Chem. Phys., 126, 084102.Google Scholar
, and 1989. Green-function Monte Carlo study of quantum antiferromagnets. Phys. Rev. B, 40, 2737–2740.Google Scholar
, and 1990. Ground-state correlations of quantum antiferromag- nets: a Green-function Monte Carlo study. Phys. Rev. B, 41, 4552–4569.Google Scholar
2010. Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press.
, and 2005. Energy and variance optimization of many-body wave functions. Phys. Rev. Lett., 94, 150201.Google Scholar
, , and 1988. Optimized trial wave functions for quantum Monte Carlo calculations. Phys. Rev. Lett., 60, 1719–1722.Google Scholar
, , and 1993. A diffusion Monte Carlo algorithm with very small timestep errors. J. Chem. Phys., 99, 2865–2890.Google Scholar
, , , , and 2007. Alleviation of the fermion-sign problem by optimization of many-body wave functions. Phys. Rev. Lett., 98, 110201.Google Scholar
, , and 2009. QWalk: A quantum Monte Carlo program for electronic structure. J. Comp. Phys., 228, 3390–3404.Google Scholar
1991. Topological orders and Chern-Simons theory in strongly correlated quantum liquid. Int. J. Mod. Phys. B, 5, 1641–1648.Google Scholar
, and 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.Google Scholar
1992. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett., 69, 2863–2866.Google Scholar
R, and 2004. Real-time evolution using the density matrix renormal- ization group. Phys. Rev. Lett., 93, 076401.Google Scholar
, and J. 1998. Density matrix renormalization group study of the striped phase in the 2D t-J model. Phys. Rev. Lett., 80, 1272–1275.Google Scholar
, and 1987a. Variational Monte Carlo studies of Hubbard model. I. J. Phys. Soc. Jpn., 56, 1490–1506.Google Scholar
, and 1987b. Variational Monte Carlo studies of Hubbard model. II. J. Phys. Soc. Jpn., 56, 3582–3592.Google Scholar
, and 1990. Variational Monte Carlo studies of Hubbard model. III. Intersite correlation effects. J. Phys. Soc. Jpn., 59, 3669–3686.Google Scholar
2012. Everything you wanted to know about data analysis and fitting but were afraid to ask. arXiv:1210.3781.
, and 1988. Effective Hamiltonian for the superconducting Cu oxides. Phys. Rev. B, 37, 3759–3761.Google Scholar
, , and 1995. Constrained path quantum Monte Carlo method for fermion ground states. Phys. Rev. Lett., 74, 3652–3655.Google Scholar