In this lectures we will explore different QMC methods aimed at solving fundamental problems of quantum statistical physics and condensed matter physics (superfluidity of Bose fluids, quantum magnetism, quantum phase transitions, electronic structure calculations, etc.), with a strong accent on the quantitative as well as the conceptual insight that these methods provide. The lectures are targeted to a broad audience, encompassing students interested in condensed matter physics, material physics or statistical physics; as well as in high-energy physics or quantum chemistry.
TD sheets: TD no 1 & 2 TD no 3
slides: PIMC applications
2023-2024 EDITION
Tue. 7/11 -- 8h-10h: lecture (Amphi C) script ; video part 1 part 2
Tue. 14/11 -- 8h-10h: lecture (Amphi C) script ; video part 1 part 2
Wed. 15/11 -- 8h-10h: TD (Amphi F)
Tue. 21/11 -- 8h-10h: lecture (Amphi C) script ; video part 1 part 2
Wed. 22/11 -- 8h-10h: TD (Amphi F)
Tue. 28/11 -- 8h-10h: lecture (Amphi C) script ; video part 1 part 2
Wed. 29/11 -- 8h-10h: TD (Amphi F)
Tue. 5/12 -- 8h-10h: lecture (Amphi C) script ; video part 1 part 2
Wed. 6/12 -- 8h-10h: TD bonus ? (Amphi F)
Tue. 12/12 -- 8h-10h: lecture (Amphi C) script ; video part 1
Wed. 13/12 -- 8h-10h: bonus lecture ? (Amphi F)
Tue. 19/12 - 8h-13h (tentative) -- orals
POSSIBLE ARTICLES/BOOK CHAPTERS for the oral presentations
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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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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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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M. E. Tuckerman
Path integration via molecular dynamics AND/OR
Ab Initio Molecular Dynamics and Ab Initio Path Integrals
https://juser.fz-juelich.de/record/24560/files/NIC-Band-10.pdf
in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, Lecture Notes, J. Grotendorst, D. Marx, A. Muramatsu (Eds.))
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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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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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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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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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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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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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W. J. Huggins et al.
Unbiasing fermionic quantum Monte Carlo with a quantum computer
(see also Supplementary information)
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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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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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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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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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Yazhen Wang, Shang Wu and Jian Zou
Quantum Annealing with Markov Chain Monte Carlo Simulations and D-Wave Quantum Computers
Statistical Science 2016, Vol. 31, No. 3, 362–398
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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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T. Dornheim
Fermion sign problem in path integral Monte Carlo simulations: Quantum dots, ultracold atoms and warm dense matter
Phys. Rev. E 100, 023307 (2019)
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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)
Additional material
David Ceperley's "Opera Omnia" - link
The Worm Algorithm (M. Boninsegni): https://www.youtube.com/watch?v=T_wvLg7z7gU
Projector Quantum Monte Carlo Methods in Chemistry and Physics (C. Umrigar) https://www.youtube.com/watch?v=dmjcjxZP48A