Alhassid,, Y., Fang,, H., & Nakada,, L. (2008). Heavy deformed nuclei in the shell model Monte Carlo method. Physical Review Letters, 101, 082501.

Alhassid,, Y., Liu,, S., & Nakada,, H. (2007). Spin projection in the shell model Monte Carlo method and the spin distribution of nuclear level densities. Physical Review Letters, 99, 162504.

Al‐Saidi,, W. A., Krakauer,, H., & Zhang,, S. (2006a). Auxiliary‐field quantum Monte Carlo study of tio and mno molecules. Physical Review B, 73, 075103. https://doi.org/10.1103/PhysRevB.73.075103

Al‐Saidi,, W. A., Krakauer,, H., & Zhang,, S. (2006b). Auxiliary‐field quantum Monte Carlo study of first‐ and second‐row post‐d elements. The Journal of Chemical Physics, 125(15), 154110. https://doi.org/10.1063/1.2357917

Al‐Saidi,, W. A., Krakauer,, H., & Zhang,, S. (2007). A study of and several H‐bonded molecules by phaseless auxiliary‐field quantum Monte Carlo with plane wave and gaussian basis sets. The Journal of Chemical Physics, 126(19), 194105. https://doi.org/10.1063/1.2735296

Al‐Saidi,, W. A., Zhang,, S., & Krakauer,, H. (2006). Auxiliary‐field quantum Monte Carlo calculations of molecular systems with a Gaussian basis. The Journal of Chemical Physics, 124(22), 224101. https://doi.org/10.1063/1.2200885

Al‐Saidi,, W. A., Zhang,, S., & Krakauer,, H. (2007). Bond breaking with auxiliary‐field quantum Monte Carlo. The Journal of Chemical Physics, 127(14), 144101. https://doi.org/10.1063/1.2770707

Anderson,, J. B., Traynor,, C. A., & Boghosian,, B. M. (1991). Quantum chemistry by random walk: Exact treatment of many‐electron systems. The Journal of Chemical Physics, 95(10), 7418–7425. https://doi.org/10.1063/1.461368

Aquilante,, F., de Vico,, L., Ferré,, N., Ghigo,, G., Malmqvist,, P.‐Å., Neogrády,, P., … Lindh,, R. (2010). Molcas 7: The next generation. Journal of Computational Chemistry, 31(1), 224–247. https://doi.org/10.1002/jcc.21318

Balian,, R., & Brezin,, E. (1969). Nonunitary Bogoliubov transformations and extension of Wick`s theorem. Nuovo Cimento B, 64, 37.

Bartlett,, R. J., & Musial,, M. (2007). Coupled‐cluster theory in quantum chemistry. Reviews of Modern Physics, 79, 291. https://doi.org/10.1103/RevModPhys.79.291

Beebe,, N. H. F., & Linderberg,, J. (1977). Simplifications in the generation and transformation of two‐electron integrals in molecular calculations. International Journal of Quantum Chemistry, 12(4), 683–705. https://doi.org/10.1002/qua.560120408

Blankenbecler,, R., Scalapino,, D. J., & Sugar,, R. L. (1981). Monte Carlo calculations of coupled boson‐fermion systems. I. Physical Review D, 24, 2278–2286. https://doi.org/10.1103/PhysRevD.24.2278

Bondybey,, V. E., & English,, J. H. (1983). Electronic structure and vibrational frequency of Cr. Chemical Physics Letters, 94, 443–447.

Booth,, G. H., Gruneis,, A., Kresse,, G., & Alavi,, A. (2013). Towards an exact description of electronic wavefunctions in real solids. Nature, 493(7432), 365–370. https://doi.org/10.1038/nature11770

Booth,, G. H., Thom,, A. J. W., & Alavi,, A. (2009). Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space. The Journal of Chemical Physics, 131(5), 054106. https://doi.org/10.1063/1.3193710

Born,, M., & Oppenheimer,, R. (1927). Zur Quantentheorie der Molekeln. Annalen der Physik, 389, 457–484.

Calandra Buonaura,, M., & Sorella,, S. (1998). Numerical study of the two‐dimensional heisenberg model using a green function Monte Carlo technique with a fixed number of walkers. Physical Review B, 57, 11446–11456. https://doi.org/10.1103/PhysRevB.57.11446

Calandra,, M., Becca,, F., & Sorella,, S. (1998). Charge fluctuations close to phase separation in the two‐dimensional model. Physical Review Letters, 81, 5185–5188. https://doi.org/10.1103/PhysRevLett.81.5185

Carlson,, J., Gandolfi,, S., Schmidt,, K. E., & Zhang,, S. (2011). Auxiliary‐field quantum Monte Carlo method for strongly paired fermions. Physical Review A, 84, 061602. https://doi.org/10.1103/PhysRevA.84.061602

Carlson,, J., Gubernatis,, J. E., Ortiz,, G., & Zhang,, S. (1999). Issues and observations on applications of the constrained‐path Monte Carlo method to many‐fermion systems. Physical Review B, 59, 12788–12798. https://doi.org/10.1103/PhysRevB.59.12788

Casey,, S. M., & Leopold,, D. G. (1993). Negative ion photoelectron spectroscopy of chromium dimer. The Journal of Physical Chemistry, 97(4), 816–830. https://doi.org/10.1021/j100106a005

Chan,, G. K.‐L., & Head‐Gordon,, M. (2002). Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group. The Journal of Chemical Physics, 116(11), 4462–4476.

Chan,, G. K.‐L., Keselman,, A., Nakatani,, N., Li,, Z., & White,, S. R. (2016). Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms. The Journal of Chemical Physics, 145(1), 014102.

Chang,, C.‐C., Rubenstein,, B. R., & Morales,, M. A. (2016). Auxiliary‐field‐based trial wave functions in quantum Monte Carlo calculations. Physical Review B, 94, 235144.

Dunning,, T. H. (1989). Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. The Journal of Chemical Physics, 90(2), 1007–1023. https://doi.org/10.1063/1.456153

Esler,, K. P., Kim,, J., Ceperley,, D. M., Purwanto,, W., Walter,, E. J., Krakauer,, H., … Srinivasan,, A. (2008). Quantum Monte Carlo algorithms for electronic structure at the petascale: The Endstation project. Journal of Physics: Conference Series, 125(1), 012057.

Fahy,, S., & Hamann,, D. R. (1991). Diffusive behavior of states in the Hubbard–Stratonovitch transformation. Physical Review B, 43, 765–779. https://doi.org/10.1103/PhysRevB.43.765

Fahy,, S. B., & Hamann,, D. R. (1990). Positive‐projection Monte Carlo simulation: A new variational approach to strongly interacting fermion systems. Physical Review Letters, 65, 3437–3440. https://doi.org/10.1103/PhysRevLett.65.3437

Feldbacher,, M., & Assaad,, F. F. (2001). Efficient calculation of imaginary‐time‐displaced correlation functions in the projector auxiliary‐field quantum Monte Carlo algorithm. Physical Review B, 63, 073105.

Feller,, D. (1992). Application of systematic sequences of wave functions to the water dimer. The Journal of Chemical Physics, 96(8), 6104–6114. https://doi.org/10.1063/1.462652

Feynman,, R., Hibbs,, A., & Styer,, D. (2010). Quantum Mechanics and Path Integrals *Dover Books on Physics* (). Dover Publications. Retrieved from https://books.google.com/books?id=JkMuDAAAQBAJ

Foulkes,, W. M. C., Mitas,, L., Needs,, R. J., & Rajagopal,, G. (2001). Quantum Monte Carlo simulations of solids. Reviews of Modern Physics, 73, 33–83. https://doi.org/10.1103/RevModPhys.73.33

Hammersley,, J. M., & Morton,, K. W. (1954). Poor man`s Monte Carlo. Journal of the Royal Statistical Society: Series B, 16(1), 23–38.

Helgaker,, T., Klopper,, W., Koch,, H., & Noga,, J. (1997). Basis‐set convergence of correlated calculations on water. The Journal of Chemical Physics, 106(23), 9639–9646. https://doi.org/10.1063/1.473863

Hirsch,, J. E. (1985). Two‐dimensional hubbard model: Numerical simulation study. Physical Review B, 31, 4403–4419. https://doi.org/10.1103/PhysRevB.31.4403

Holmes,, A. A., Tubman,, N. M., & Umrigar,, C. J. (2016). Heat‐bath configuration interaction: An efficient selected configuration interaction algorithm inspired by heat‐bath sampling. J. Chem. Theor. Comput., 12, 3674–3680.

Hubbard,, J. (1959). Calculation of partition functions. Physical Review Letters, 3, 77–78. https://doi.org/10.1103/PhysRevLett.3.77

Knizia,, G., & Chan,, G. K.‐L. (2012). Density matrix embedding: A simple alternative to dynamical mean‐field theory. Physical Review Letters, 109, 186404. https://doi.org/10.1103/PhysRevLett.109.186404

Koch,, H., de Meras,, A. S., & Pedersen,, T. B. (2003). Reduced scaling in electronic structure calculations using cholesky decompositions. The Journal of Chemical Physics, 118(21), 9481–9484. https://doi.org/10.1063/1.1578621

Kohn,, W. (1999). Nobel lecture: Electronic structure of matter: Wave functions and density functionals. Reviews of Modern Physics, 71, 1253–1266. https://doi.org/10.1103/RevModPhys.71.1253

Kong,, L., Bischoff,, F. A., & Valeev,, E. F. (2012). Explicitly correlated R12/F12 methods for electronic structure. Chemical Reviews, 112(1), 75–107. https://doi.org/10.1021/cr200204r

Kraus,, D., Lorenz,, M., & Bondybey,, V. E. (2001). On the dimers of the VIB group: a new NIR electronic state of Mo. PhysChemComm, 4, 44–48. https://doi.org/10.1039/B104063B

Kurashige,, Y., Chan,, G. K.‐L., & Yanai,, T. (2013). Entangled quantum electronic wavefunctions of the MnCao cluster in photosystem II. Nature Chemistry, 5(8), 660–666. https://doi.org/10.1038/nchem.1677

Kwee,, H., Zhang,, S., & Krakauer,, H. (2008). Finite‐size correction in many‐body electronic structure calculations. Physical Review Letters, 100, 126404. https://doi.org/10.1103/PhysRevLett.100.126404

LeBlanc,, J. P. F., Antipov,, A. E., Becca,, F., Bulik,, I. W., Chan,, G. K.‐L., Chung,, C.‐M., … Gull,, E. (2015). Solutions of the two‐dimensional hubbard model: Benchmarks and results from a wide range of numerical algorithms. Physical Review X, 5, 041041. https://doi.org/10.1103/PhysRevX.5.041041

Loh,, E. Y., Gubernatis,, J. E., Scalettar,, R. T., White,, S. R., Scalapino,, D. J., & Sugar,, R. L. (1990). Sign problem in the numerical simulation of many‐electron systems. Physical Review B, 41, 9301–9307. https://doi.org/10.1103/PhysRevB.41.9301

Ma,, F., Purwanto,, W., Zhang,, S., & Krakauer,, H. (2015). Quantum Monte Carlo calculations in solids with downfolded Hamiltonians. Physical Review Letters, 114, 226401. https://doi.org/10.1103/PhysRevLett.114.226401

Ma,, F., Zhang,, S., & Krakauer,, H. (2013). Excited state calculations in solids by auxiliary‐field quantum Monte Carlo. New Journal of Physics, 15(9), 093017.

Ma,, F., Zhang,, S., & Krakauer,, H. (2017). Auxiliary‐field quantum Monte Carlo calculations with multiple‐projector pseudopotentials. Physical Review B, 95, 165103. https://doi.org/10.1103/PhysRevB.95.165103

Martin,, R. M. (2004). Electronic structure: Basic theory and practical methods. Cambridge, England: Cambridge University Press.

Motta,, M., Ceperley,, D. M., Chan,, G. K.‐L., Gomez,, J. A., Gull,, E., Guo,, S., … Zhang,, S. (2017). Towards the solution of the many‐electron problem in real materials: Equation of state of the hydrogen chain with state‐of‐the‐art many‐body methods. Physical Review X, 7, 031059. https://doi.org/10.1103/PhysRevX.7.031059

Motta,, M., Galli,, D. E., Moroni,, S., & Vitali,, E. (2014). Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo. The Journal of Chemical Physics, 140(2), 024107. https://doi.org/10.1063/1.4861227

Motta,, M., & Zhang,, S. (2017). Computation of ground‐state properties in molecular systems: Back‐propagation with auxiliary‐field quantum Monte Carlo. Journal of Chemical Theory and Computation, 13, 5367–5378.

Motta,, M., & Zhang,, S. (2018a). *Acceleration of auxiliary‐field quantum Monte Carlo calculations via tensor hypercontraction.* In preparation.

Motta,, M., & Zhang,, S. (2018b). Calculation of interatomic forces and optimization of molecular geometry with auxiliary‐field quantum Monte Carlo. *The Journal of Chemical Physics*, 148(18), 181101. https://doi.org/10.1063/1.5029508

Musial,, M., & Bartlett,, R. J. (2005). Critical comparison of various connected quadruple excitation approximations in the coupled‐cluster treatment of bond breaking. The Journal of Chemical Physics, 122(22), 224102. https://doi.org/10.1063/1.1926273

Nakada,, H., & Alhassid,, Y. (1997). Total and parity‐projected level densities iron‐region nuclei in the auxiliary fields Monte Carlo shell model. Physical Review Letters, 79, 2939–2942.

Nguyen,, H., Shi,, H., Xu,, J., & Zhang,, S. (2014). Cpmc‐lab: A matlab package for constrained path Monte Carlo calculations. Computer Physics Communications, 185(12), 3344–3357.

Olivares‐Amaya,, R., Hu,, W., Nakatani,, N., Sharma,, S., Yang,, J., & Chan,, G. K.‐L. (2015). The ab‐initio density matrix renormalization group in practice. The Journal of Chemical Physics, 142(3), 034102.

Paldus,, J., & Li,, X. (1999). A critical assessment of coupled cluster method in quantum chemistry. Advances in Chemical Physics, 110, 1. https://doi.org/10.1002/9780470141694.ch1/summary

Peterson,, K. A. (2003). Systematically convergent basis sets with relativistic pseudopotentials. I. correlation consistent basis sets for the post‐d group 13–15 elements. The Journal of Chemical Physics, 119(21), 11099–11112. https://doi.org/10.1063/1.1622923

Peterson,, K. A., Figgen,, D., Goll,, E., Stoll,, H., & Dolg,, M. (2003). Systematically convergent basis sets with relativistic pseudopotentials. II. small‐core pseudopotentials and correlation consistent basis sets for the post‐d group 16–18 elements. The Journal of Chemical Physics, 119(21), 11113–11123. https://doi.org/10.1063/1.1622924

Press,, W. (2007). Numerical recipes 3rd edition: The art of scientific computing. Cambridge University Press.

Purwanto,, W., Al‐Saidi,, W. A., Krakauer,, H., & Zhang,, S. (2008). Eliminating spin contamination in auxiliary‐field quantum Monte Carlo: Realistic potential energy curve of F(2). The Journal of Chemical Physics, 128(11), 114309. https://doi.org/10.1063/1.2838983

Purwanto,, W., Krakauer,, H., Virgus,, Y., & Zhang,, S. (2011). Assessing weak hydrogen binding on Ca centers: an accurate many‐body study with large basis sets. The Journal of Chemical Physics, 135(16), 164105. https://doi.org/10.1063/1.3654002

Purwanto,, W., Krakauer,, H., & Zhang,, S. (2009). Pressure‐induced diamond to ‐tin transition in bulk silicon: A quantum Monte Carlo study. Physical Review B, 80, 214116. https://doi.org/10.1103/PhysRevB.80.214116

Purwanto,, W., & Zhang,, S. (2004). Quantum Monte Carlo method for the ground state of many‐boson systems. Physical Review E, 70, 056702. https://doi.org/10.1103/PhysRevE.70.056702

Purwanto,, W., Zhang,, S., & Krakauer,, H. (2009). Excited state calculations using phaseless auxiliary‐field quantum Monte Carlo: Potential energy curves of low‐lying C singlet states. The Journal of Chemical Physics, 130(9), 094107. https://doi.org/10.1063/1.3077920

Purwanto,, W., Zhang,, S., & Krakauer,, H. (2013). Frozen‐orbital and downfolding calculations with auxiliary‐field quantum Monte Carlo. Journal of Chemical Theory and Computation, 9(11), 4825–4833. https://doi.org/10.1021/ct4006486

Purwanto,, W., Zhang,, S., & Krakauer,, H. (2015). An auxiliary‐field quantum Monte Carlo study of the chromium dimer. The Journal of Chemical Physics, 142(6), 064302. https://doi.org/10.1063/1.4906829

Purwanto,, W., Zhang,, S., & Krakauer,, H. (2016). Auxiliary‐field quantum Monte Carlo calculations of the molybdenum dimer. The Journal of Chemical Physics, 144(24), 244306. https://doi.org/10.1063/1.4954245

Qin,, M., Shi,, H., & Zhang,, S. (2016). Coupling quantum Monte Carlo and independent‐particle calculations: Self‐consistent constraint for the sign problem based on the density or the density matrix. Physical Review B, 94, 235119. https://doi.org/10.1103/PhysRevB.94.235119

Reynolds,, P. J., Ceperley,, D. M., Alder,, B. J., & Lester,, W. A. (1982). Fixed‐node quantum Monte Carlo for molecules. Journal of Chemical Physics, 77(11), 5593–5603. https://doi.org/10.1063/1.443766

Rom,, N., Charutz,, D., & Neuhauser,, D. (1997). Shifted‐contour auxiliary‐field Monte Carlo: circumventing the sign difficulty for electronic‐structure calculations. Chemical Physics Letters, 270(3), 382–386.

Rosenberg,, P., Shi,, H., & Zhang,, S. (2017). Ultracold atoms in a square lattice with spin–orbit coupling: Charge order, superfluidity, and topological signatures. *Physical Review Letters, 119*, 265301. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.265301

Rosenbluth,, M. N., & Rosenbluth,, A. W. (1955). Monte Carlo calculation of the average extension of molecular chains. The Journal of Chemical Physics, 23(2), 356–359. https://doi.org/10.1063/1.1741967

Rubenstein,, B. R., Zhang,, S., & Reichman,, D. R. (2012). Finite‐temperature auxiliary‐field quantum Monte Carlo technique for Bose‐Fermi mixtures. Physical Review A, 86, 053606.

Schmidt,, K. E., & Kalos,, M. H. (1984). Chapter 4: Few‐ and many‐fermion problems. In K. Binder, (Ed.), Applications of the Monte Carlo Method in statistical physics. Heidelberg: Springer Verlag.

Schmidt,, M. W., Baldridge,, K. K., Boatz,, J. A., Elbert,, S. T., Gordon,, M. S., Jensen,, J. H., … Montgomery,, J. A. (1993). General atomic and molecular electronic structure system. Journal of Computational Chemistry, 14(11), 1347–1363. https://doi.org/10.1002/jcc.540141112

Schuch,, N., & Verstraete,, F. (2009). Computational complexity of interacting electrons and fundamental limitations of density functional theory. Nature Physics, 5(10), 732–735. https://doi.org/10.1038/nphys1370

Sharma,, S., Holmes,, A. A., Jeanmairet,, G., Alavi,, A., & Umrigar,, C. J. (2017). Semistochastic heat‐bath configuration interaction method: Selected configuration interaction with semistochastic perturbation theory. Journal of Chemical Theory and Computation, 13, 1595–1604.

Shavitt,, I., & Bartlett,, R. J. (2009). Many‐body methods in chemistry and physics. New York, NY: Cambridge University Press. Retrieved from http://admin.cambridge.org/ms/academic/subjects/Chemistry/physical-Chemistry/many-body-methods-Chemistry-and-physics-mbpt-and-coupled-cluster-theory?format=HB

Shee,, J., Zhang,, S., Reichman,, D. R., & Friesner,, R. A. (2017). Chemical transformations approaching chemical accuracy via correlated sampling in auxiliary‐field quantum Monte Carlo. Journal of Chemical Theory and Computation, 13(6), 2667–2680. https://doi.org/10.1021/acs.jctc.7b00224

Sherman,, J., & Morrison,, W. J. (1949). Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix. Annals of Mathematical Statistics, 20, 620–624. https://doi.org/10.1214/aoms/1177729959

Shi,, H., Chiesa,, S., & Zhang,, S. (2015). Ground‐state properties of strongly interacting Fermi gases in two dimensions. Physical Review A, 92, 033603. https://doi.org/10.1103/PhysRevA.92.033603

Shi,, H., Jiménez‐Hoyos,, C. A., Rodriguez‐Guzmán,, R., Scuseria,, G. E., & Zhang,, S. (2014). Symmetry‐projected wave functions in quantum Monte Carlo calculations. Physical Review B, 89, 125129. https://doi.org/10.1103/PhysRevB.89.125129

Shi,, H., & Zhang,, S. (2013). Symmetry in auxiliary‐field quantum Monte Carlo calculations. Physical Review B, 88, 125132. https://doi.org/10.1103/PhysRevB.88.125132

Shi,, H., & Zhang,, S. (2017). Many‐body computations by stochastic sampling in Hartree‐Fock‐Bogoliubov space. Physical Review B, 95, 045144. https://doi.org/10.1103/PhysRevB.95.045144

Shi,, H., & Zhang,, S. (2018). *Accelerating the use of multi‐determinant trial wave functions in auxiliary‐field quantum Monte Carlo calculations.* In preparation.

Silvestrelli,, P. L., Baroni,, S., & Car,, R. (1993). Auxiliary‐field quantum Monte Carlo calculations for systems with long‐range repulsive interactions. Physical Review Letters, 71, 1148–1151. https://doi.org/10.1103/PhysRevLett.71.1148

Simard,, B., Lebeault‐Dorget,, M.‐A., Marijnissen,, A. M., & Meulen,, J. J. (1998). Photoionization spectroscopy of dichromium and dimolybdenum: Ionization potentials and bond energies. The Journal of Chemical Physics, 108(23), 9668–9674. https://doi.org/10.1063/1.476442

Sorella,, S. (2011). Linearized auxiliary fields Monte Carlo technique: Efficient sampling of the fermion sign. Physical Review B, 84, 241110(R).

Stratonovich,, R. L. (1958). On a method of calculating quantum distribution functions. Soviet Physics Doklady, 2, 416.

Suewattana,, M., Purwanto,, W., Zhang,, S., Krakauer,, H., & Walter,, E. J. (2007). Phaseless auxiliary‐field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules. Physical Review B, 75, 245123. https://doi.org/10.1103/PhysRevB.75.245123

Sugiyama,, G., & Koonin,, S. (1986). Auxiliary field monte‐carlo for quantum many‐body ground states. Annals of Physics, 168(1), 1–26.

Sun,, Q., Berkelbach,, T. C., Blunt,, N. S., Booth,, G. H., Guo,, S., Li,, Z., … Chan,, G. K.‐L. (2018). PySCF: The python‐based simulations of chemistry framework. WIREs Computational Molecular Science, 8, e1340.

Suzuki,, M. (1976). Relationship between d‐dimensional quantal spin systems and (d+1)‐dimensional ising systemsequivalence, critical exponents and systematic approximants of the partition function and spin correlations. Progress of Theoretical Physics, 56(5), 1454–1469.

Szabo,, A., & Ostlund,, N. (1989). Modern quantum chemistry: Introduction to advanced electronic structure theory *Dover Books on Chemistry* (). Dover Publications.

Thouless,, D. (1960). Stability conditions and nuclear rotations in the Hartree‐Fock theory. Nuclear Physics, 21, 225–232.

Thouless,, D. (1961). Vibrational states of nuclei in the random phase approximation. Nuclear Physics, 22(1), 78–95.

Trivedi,, N., & Ceperley,, D. M. (1989). Green‐function Monte Carlo study of quantum antiferromagnets. Physical Review B, 40, 2737–2740. https://doi.org/10.1103/PhysRevB.40.2737

Trotter,, H. (1959). On the product of semi‐groups of operators. Proceedings of the American Mathematical Society, 10, 545–551.

Troyer,, M., & Wiese,, U. J. (2005). Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Physical Review Letters, 94, 170201. https://doi.org/10.1103/PhysRevLett.94.170201

Tubman,, N. M., Lee,, J., Takeshita,, T. Y., Head‐Gordon,, M., & Whaley,, K. B. (2016). A deterministic alternative to the full configuration interaction quantum Monte Carlo. The Journal of Chemical Physics, 145, 044112.

Ulmke,, M., & Scalettar,, R. T. (2000). Auxiliary‐field Monte Carlo for quantum spin and boson systems. Physical Review B, 61, 9607–9612.

Umrigar,, C. J., Nightingale,, M. P., & Runge,, K. J. (1993). A diffusion Monte Carlo algorithm with very small time‐step errors. The Journal of Chemical Physics, 99(4), 2865–2890. https://doi.org/10.1063/1.465195

Valiev,, M., Bylaska,, E., Govind,, N., Kowalski,, K., Straatsma,, T., Dam,, H. V., … de Jong,, W. (2010). NWChem: A comprehensive and scalable open‐source solution for large scale molecular simulations. Computer Physics Communications, 181(9), 1477–1489.

Virgus,, Y., Purwanto,, W., Krakauer,, H., & Zhang,, S. (2012). Ab initio many‐body study of cobalt adatoms adsorbed on graphene. Physical Review B, 86, 241406. https://doi.org/10.1103/PhysRevB.86.241406

Vitali,, E., Shi,, H., Qin,, M., & Zhang,, S. (2016). Computation of dynamical correlation functions for many‐fermion systems with auxiliary‐field quantum Monte Carlo. Physical Review B, 94, 085140. https://doi.org/10.1103/PhysRevB.94.085140

White,, S. R. (1992). Density matrix formulation for quantum renormalization groups. Physical Review Letters, 69(19), 2863–2866. https://doi.org/10.1103/PhysRevLett.69.2863

White,, S. R., & Martin,, R. L. (1999). Ab initio quantum chemistry using the density matrix renormalization group. The Journal of Chemical Physics, 110(9), 4127–4130.

Wick,, G. C. (1950). The evaluation of the collision matrix. Physics Review, 80, 268–272. https://doi.org/10.1103/PhysRev.80.268

Wilson,, M. T., & Gyorffy,, B. L. (1995). Auxiliary‐field quantum Monte Carlo calculations for the relativistic electron gas. Journal of Physics: Condensed Matter, 7(8), 1565.

Woon,, D. E., & Dunning,, T. H. (1993). Benchmark calculations with correlated molecular wave functions. I. multireference configuration interaction calculations for the second row diatomic hydrides. The Journal of Chemical Physics, 99(3), 1914–1929. https://doi.org/10.1063/1.465306

Yang,, J., Hu,, W., Usvyat,, D., Matthews,, D., Schütz,, M., & Chan,, G. K.‐L. (2014). Ab initio determination of the crystalline benzene lattice energy to sub‐kilojoule/mole accuracy. Science, 345(6197), 640–643.

Zhang,, S. (1999). Finite‐temperature Monte Carlo calculations for systems with fermions. Physical Review Letters, 83, 2777–2780. https://doi.org/10.1103/PhysRevLett.83.2777

Zhang,, S. (2013). Chapter 15: Auxiliary‐field quantum Monte Carlo for correlated electron systems. In E. P. E. Koch, & U. Schollwöck, (Eds.), Emergent phenomena in correlated matter: Modeling and simulation. Verlag des Forschungszentrum Jülich. Retrieved from https://www.cond-mat.de/events/correl13/manuscripts/zhang.pdf

Zhang,, S., Carlson,, J., & Gubernatis,, J. E. (1995). Constrained path quantum Monte Carlo method for fermion ground states. Physical Review Letters, 74, 3652–3655. https://doi.org/10.1103/PhysRevLett.74.3652

Zhang,, S., Carlson,, J., & Gubernatis,, J. E. (1997). Constrained path Monte Carlo method for fermion ground states. Physical Review B, 55, 7464–7477. https://doi.org/10.1103/PhysRevB.55.7464

Zhang,, S., & Kalos,, M. H. (1991). Exact Monte Carlo calculation for few‐electron systems. Physical Review Letters, 67, 3074–3077. https://doi.org/10.1103/PhysRevLett.67.3074

Zhang,, S., & Krakauer,, H. (2003). Quantum Monte Carlo method using phase‐free random walks with Slater determinants. Physical Review Letters, 90, 136401. https://doi.org/10.1103/PhysRevLett.90.136401

Zhang,, S., Krakauer,, H., Al‐Saidi,, W. A., & Suewattana,, M. (2005). Quantum simulations of realistic systems by auxiliary fields. Computer Physics Communications, 169(1–3), 394–399.

Zheng,, B.‐X., Chung,, C.‐M., Corboz,, P., Ehlers,, G., Noack,, R. M., Shi,, H., … Chan,, G. K.‐L. (2017). Stripe order in the underdoped region of the two‐dimensional Hubbard model. *Science*, *358*, 1155. http://science.sciencemag.org/content/358/6367/1155

Zheng,, B.‐X., Kretchmer,, J. S., Shi,, H., Zhang,, S., & Chan,, G. K.‐L. (2017). Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary‐field quantum Monte Carlo solver. Physical Review B, 95, 045103. https://doi.org/10.1103/PhysRevB.95.045103