Auxiliary field methods (120' lecture)

Shiwei Zhang

Link to Presentation slides (in PPT or PDF) format: AF-QMC_LectNotes_2007_Zhang.pdf

Tentative outline

• Why auxiliary-field (AF) methods?
  • Why use Slater determinants as random walkers?
  • What is their relation to diffusion Monte Carlo (DMC)? To path-integral Monte Carlo?
  • What is their relation to mean-field methods?
  • Toy problem to set up "the language"
• Standard AF QMC and the sign problem
• New framework: stochastic mean-field theory
  • branching random walks in Slater determinant space
  • boson systems?
• BREAK
• The constrained path approximation for model Hamiltonians
  • ground-state calculations
  • finite-temperature formulation
  • applications to Hubbard-like models
• The Phaseless approximation for realistic Hamiltonians
• Applications to electronic systems
  • molecules and solids using plane-wave basis and pseudopotentials
  • atoms and molecules using Gaussian basis sets
• Discussion

Some References

• Lecture Notes: (missing recent developments – see papers below)
  1. Shiwei Zhang, ``Constrained Path Monte Carlo For Fermions,'' in ``Quantum Monte Carlo Methods in Physics and Chemistry,'' Ed.M. P. Nightingale and C. J. Umrigar, NATO ASI Series (Kluwer Academic Publishers, 1998).
     (cond-mat/9909090: http://xxx.lanl.gov/abs/cond-mat/9909090v1 )
  2. Shiwei Zhang, ``Quantum Monte Carlo Methods for Strongly Correlated Electron Systems,'' in ``Theoretical Methods for Strongly Correlated Electrons,'' Ed. by D. Senechal, A.-M. Tremblay, and C. Bourbonnais, Springer-Verlag (2003).
     (available at my website: http://www.physics.wm.edu/~shiwei/Preprint/Springer03.pdf )
• Some papers: (in addition to the general QMC references from previous lectures)
  1. R. Blankenbecler, D. J. Scalapino, and R. L. Sugar, Phys. Rev. D 24, 2278 (1981)
  2. G. Sugiyama and S. E. Koonin, Ann. Phys. 168, 1 (1986)
  3. S. R. White et. al., Phys. Rev. B 40, 506 (1989)
  4. D. R. Hamann and S. B. Fahy, Phys. Rev. B 41, 11352 (1990)
  5. P. L. Silvestrelli and S. Baroni and R. Car, Phys. Rev. Lett. 71, 1148 (1993)
  6. N. Rom, D.M. Charutz, and D. Neuhauser, Chem. Phys. Lett. 270, 382 (1997).
  7. S. Zhang and J. Carlson and J. E. Gubernatis, Phys. Rev. B 55, 7464 (1997)
  8. S. Zhang, Phys. Rev. Lett. 83, 2777 (1999)
  9. S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003)
  10. W. Purwanto and S. Zhang, Phys. Rev. E 70, 056702 (2004)
  11. W. A. Al-Saidi, S. Zhang, and H. Krakauer, J. Chem. Phys. 124, 224101 (2006)

Comments

Some comments from instructor, such as prerequisite reading.