Program for the 2024-2025 edition
05/11/2024 lecture (2h) T. Roscilde (introduction + exact diagonalization) script videos part 1 part 2
06/11/2024 lecture (2h) T. Roscilde (exact diagonalization) script videos part 1 part 2
12/11/2024 lecture (2h) F. Mezzacapo (Variational Monte Carlo) script
13/11/2024 lecture (2h) F. Mezzacapo (Variational Monte Carlo) script
20/11/2024 lecture (2h) F. Mezzacapo (Diffusion Monte Carlo)
21/11/2024 lecture (2h) F. Mezzacapo (Diffusion Monte Carlo)
26/11/2024 lecture (2h) T. Roscilde (Matrix-product states) script videos part 1 part 2
27/11/2024 lecture (2h) T. Roscilde (Matrix-product states) script videos part 1 part 2
3/12/2024 lecture (2h) F. Mezzacapo (Path Integral Monte Carlo)
4/12/2024 lecture (2h) F. Mezzacapo (Path Integral Monte Carlo)
10/12/2024 lecture (2h) T. Roscilde (Quantum Monte Carlo for lattice systems) script videos part 1 part 2
11/12/2024 lecture (2h) T. Roscilde (Quantum Monte Carlo for lattice systems) script videos part 1 part 2
18/12/2024: orals
ARTICLES FOR THE FINAL EXAM
QUANTUM MONTE CARLO: VMC, PIMC, etc.
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Quantum chemistry
R. Assaraf and M. Caffarel
Computing Forces with Quantum Monte Carlo
J. Chem. Phys. 113, 4028 (2000)
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J. Lee, H. Q. Pham, and D. R. Reichmann
Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment of the Main Group Chemistry and Bond Breaking
https://arxiv.org/abs/2208.01280
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Michele Casula and Sandro Sorella
Geminal wave functions with Jastrow correlation: A first application to atoms
J. Chem. Phys. 119, 6500 (2003)
AND/OR
M. Casula, C. Attaccalite, and S. Sorella
Correlated geminal wave function for molecules: An efficient resonating valence bond approach
J. Chem. Phys. 121, 7110 (2004)
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Benoît Braïda; Julien Toulouse; Michel Caffarel; C. J. Umrigar
Quantum Monte Carlo with Jastrow-Valence-Bond wave functions
J. Chem. Phys. 134, 084108 (2011)
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Correlated fermions
G. Booth, A. Thom and A. Alavi
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space
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S. Zhang
Auxiliary-Field Quantum Monte Carlo for Correlated Electron Systems
https://www.cond-mat.de/events/correl13/manuscripts/zhang.pdf
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S. Zhang
Constrained Path Monte Carlo for Fermions
In: M. P. Nightingale and C. J. Umrigar, “Quantum Monte Carlo Methods in Physics and Chemistry,” Kluwer Academic Publishers, Berlin, 1999.
download here
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G. Carleo, F. Becca, S. Moroni, and S. Baroni
Reptation quantum Monte Carlo algorithm for lattice Hamiltonians with a directed-update scheme
Phys. Rev. E 82, 046710 (2010)
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S. Y. Chang, V. R. Pandharipande, J. Carlson, and K. E. Schmidt
Quantum Monte Carlo studies of superfluid Fermi gases
Phys. Rev. A 70, 043602 (2004)
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F. F. Assaad
Quantum Monte Carlo Methods on Lattices: The Determinantal Approach
https://core.ac.uk/download/pdf/35009945.pdf (In: Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, Lecture Notes, J. Grotendorst, D. Marx, A. Muramatsu (Eds.))
See also these lecture slides: http://benasque.org/2019scs/talks_contr/041_Assaad_Lectures.pdf
these lecture notes: https://pawn.physik.uni-wuerzburg.de/~assaad/Reprints/assaad_evertz.pdf
and this introductory article: http://www.scielo.br/pdf/bjp/v33n1/a03v33n1.pdf
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Z. Bai, W. Chen, R. Scalettar & I. Yamazaki
Numerical Methods for the Quantum Monte Carlo Simulations of the Hubbard Model
https://web.cs.ucdavis.edu/~bai/publications/bcsy09.pdf (in Multi-Scale Phenomena in Complex Fluids, T. Y. Hou, C. Liu and J.-G. Liu, eds., Higher Education Press, Beijing, 2009)
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K. Ido, T. Ohgoe, and M. Imada
Time-dependent many-variable variational Monte Carlo method for nonequilibrium strongly correlated electron systems
Phys. Rev. B 92, 245106 (2015)
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M. Motta et al.
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
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S. Sorella and A. Zen
The new Resonating Valence Bond Method for ab-initio Electronic Simulations
https://arxiv.org/pdf/1310.0845.pdf (in Many-electron Approaches in Physics, Chemistry and Mathematics: A Multidisciplinary View, edited by V. Bach and L. Delle Site (Springer International Publishing, Cham, 2014)
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M. Taddei, M. Ruggeri, S. Moroni, and M. Holzmann
Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids
Phys. Rev. B 91, 115106 (2015)
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Correlated bosons
Mats Wallin, Erik S. Sorensen, S. M. Girvin, and A. P. Young
Superconductor-insulator transition in two-dimensional dirty boson systems
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E. L. Pollock and D. Ceperley
Path-integral computation of superfluid densities
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Y. Kwon, F. Paesani, and K. B. Whaley
Local superfluidity in inhomogeneous quantum fluids
Phys. Rev. B 74, 174522 (2006)
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M. Boninsegni, N. V. Prokof’ev, and B. V. Svistunov
Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations
Phys. Rev. E 74, 036701 (2006)
see also this online talk
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C. M. Herdman, Stephen Inglis, P.-N. Roy, R. G. Melko, and A. Del Maestro
Path-integral Monte Carlo method for Rényi entanglement entropies
Phys. Rev. E 90, 013308 (2014)
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B. Kulchytskyy, G. Gervais, and A. Del Maestro
Local superfluidity at the nanoscale
Phys. Rev. B 88, 064512 (2013)
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S. Pilati, S. Giorgini, M. Modugno and N. Prokof’ev
Dilute Bose gas with correlated disorder: a path integral Monte Carlo study
New J. Phys. 12, 073003 (2010)
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Y. Yan and D. Blume
Path integral Monte Carlo ground state approach: formalism, implementation, and applications
J. Phys. B: At. Mol. Opt. Phys. 50 223001 (2017)
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Quantum spin systems, and general methods
G. Carleo and M. Troyer
Solving the quantum many-body problem with artificial neural networks
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F. Becca, L. Capriotti, A. Parola, and S. Sorella
Variational wavefunctions for frustrated magnetic models
https://arxiv.org/pdf/0905.4854
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H. Lange, A. Van de Walle, A. Abedinnia and A. Bohrdt
From Architectures to Applications: A Review of Neural Quantum States
https://arxiv.org/pdf/2402.09402
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Ivan Glasser, Nicola Pancotti, Moritz August, Ivan D. Rodriguez, and J. Ignacio Cirac
Neural-Network Quantum States, String-Bond States, and Chiral Topological States
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Monte Carlo Simulations of Quantum Spin Systems in the Valence Bond Basis
https://arxiv.org/pdf/0704.1469
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A. W. Sandvik and G. Vidal
Variational Quantum Monte Carlo simulations with Tensor Network States
Phys. Rev. Lett. 99, 220602 (2007)
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A. King et al.
Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets
Nature Communications 12, 1113 (2021)
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J. R. McClean et al.
The theory of variational hybrid quantum-classical algorithms
New J. Phys. 18, 023023 (2016)
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Olav F. Syljuåsen and Anders W. Sandvik
Quantum Monte Carlo with directed loops
Phys. Rev. E 66, 046701 (2002)
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E. M. Inack, G. Giudici, T. Parolini, G. Santoro, and S. Pilati
Understanding quantum tunneling using diffusion Monte Carlo simulations
Phys. Rev. A 97, 032307 (2018)
see also this online talk
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More on methods
M. Jarrell
Maximum Entropy Analytic Continuation of Quantum Monte Carlo Data
http://www.phys.lsu.edu/~jarrell/Green/MEM_Salerno.pdf (in Lectures on the Physics of Strongly Correlated Systems XII AIP Conference Proc., Eds. A. Avella and F. Mancini, 2008)
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A. S. Mishchenko
Stochastic Optimization Method for Analytic Continuation
https://www.cond-mat.de/events/correl12/manuscripts/mishchenko.pdf (in E. Pavarini, E. Koch, F. Anders, and M. Jarrell, Correlated Electrons: From Models to Materials, Modeling and Simulation Vol. 2)
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EXACT DIAGONALIZATION, MATRIX-PRODUCT STATES / TENSOR-NETWORK STATES
P. Prelovsek, J. Bonca
Ground state and FInite Temperature Lanczos Method
https://arxiv.org/abs/1111.5931
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S. R. White
Density-matrix algorithms for quantum renormalization groups
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A. Feiguin
The Density-Matrix Renormalization Group and Its Time-Dependent Variants
http://physics.uwyo.edu/~adrian/dmrg_lectures.pdf
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Tom Vieijra, Jutho Haegeman, Frank Verstraete, and Laurens Vanderstraeten
Direct sampling of projected entangled-pair states
Phys. Rev. B 104, 235141 (2021)
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A. W. Sandvik and G. Vidal
Variational Quantum Monte Carlo simulations with Tensor Network States
Phys. Rev. Lett. 99, 220602 (2007)
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P. Corboz
Variational optimization with infinite projected entangled-pair states
Phys. Rev. B 94, 035133 (2016)
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M. Lubasch, J. I. Cirac, and M.-C. Bañuls
Algorithms for finite projected entangled pair states
Phys. Rev. B 90, 064425 (2014)
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M. Binder and T. Barthel
Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution
Phys. Rev. B 92, 125119 (2015)
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G. K-L. Chan, A. Keselman, N. Nakatani, Z. Li, S. R. White
Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms
J. Chem. Phys. 145, 014102 (2016)
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G. K.-L. Chan and S. Sharma
The Density Matrix Renormalization Group in Quantum Chemistry
ANNUAL REVIEW OF PHYSICAL CHEMISTRY Volume 62, 2011
BONUS MATERIAL