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Physics 880.05 Many-Body Physics:
EFT, RG, and Computation
Autumn, 2009

Welcome to the Physics 880.05 Many-Body Physics: EFT, RG, and Computation home page!
URL: http://www.physics.ohio-state.edu/physics/ntg/880_2009/manybody.php
The course information is available here plus lots of supplementary info. Please check this page regularly.

Recent changes to this page:



Background or Supplementary Readings

ReadingTopicReading Due
excerpt from Suzuki/Varga chapter 3 "Introduction to Variational Methods" (for SVM discussion) 09/28/09
overview of SVM "Stochastic variational methods in few-body systems" by Suzuki, Varga, Usukura 09/28/09
excerpt from Morse, Thermal Physics chapter 8 Thermodynamic potentials and Legendre transformations between them, including for "extra" pairs of variables. 09/28/09
excerpts from F&W chapter two Statistical mechanics review and application to non-interacting Fermi and Bose gases in second quantization 09/28/09
excerpt from Zinn-Justin chapter 1 Summary of formulas for gaussian integration, including Grassmann variables. 09/30/09
excerpts from Negele/Orland text Functional integral formulation; basics of perturbation theory with path integrals 10/08/09
excerpt from Atland/Simons text Functional integral formulation for quantum mechanics. 10/08/09
Notes from 780.20 on Monte Carlo methods Excerpts from the class notes for Computational Physics on random numbers, Monte Carlo methods, the Metropolis algorithm, and more. 10/18/09
excerpts from Negele/Orland text Coherent states and Gaussian integrals 10/21/09
excerpts from Negele/Orland text Hugenholtz diagrams and Feynman rules 10/21/09
excerpts from Negele/Orland text Irreducible diagrams and integral equations 11/04/09

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Problem Sets and Hints

Click on the problem set number to get a pdf copy of the assignment.

Due Date(s)AssignmentCommentsSolutions
10/12/09 and 10/16/09 #1 Hints, suggestions, etc. solutions
10/27/09 and 10/30/09 #2 Programs: svm_test.zip, MCIntEval.zip, expm_demos.zip. Hints, suggestions, etc. solutions
11/24/09 #3 Hints, suggestions, etc. solutions
12/11/09 #4 Programs: one_d_fermions.zip. Notes on computing observables. Hints, suggestions, etc. solutions

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PDF Copies of Handouts

Date OutHandoutComments
23-Sep-2009 overview 1 Graphs of phenomenological central nucleon-nucleon potential and potential between He-3 atoms plus lattice QCD calculations.
23-Sep-2009 overview 2 Nuclear three-body forces.
23-Sep-2009 overview 3 Nuclear dof's and Weinberg RG quote
23-Sep-2009 overview 4 Digital potential and resolution analogy
23-Sep-2009 overview 5 Full Configuration Interaction (FCI) scaling with basis size (from James Vary talk, 2008)
28-Sep-2009 Sample SVM results Some figures and tables from the Suzuki/Varga SVM book.
28-Sep-2009 Ill-conditioning example A simple MATLAB example of an ill-conditioned matrix because of near linear dependence (as encountered with the SVM).
30-Sep-2009 Approximations to model Z Error plots for approximations to a simple integral that serves as a model partition function. Ordinary perturbation theory is compared to expanding about saddlepoints (one in this case).
02-Oct-2009 Using MATLAB for Linear Algebra Summary guide to using MATLAB matrix functions.

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Xeroxed Handouts

This is a list of excerpts from texts or review articles handed out in class (extras are available from Prof. Furnstahl). In most cases, they can't be scanned because of copyright issues, but there will be some that have links to downloadable versions (e.g., from the arXiv).

Date OutHandoutComments
23-Sep-2009 First pages from review article "Effective Field Theory and Finite-Density Systems"
23-Sep-2009 First pages from Blume/Daily article "Illustration of universal relations for trapped four-fermion system with arbitrary s-wave scattering length"

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Class Notes

The notes are in PDF format only.

Class DateNotesComments
23-Sep-2009 lecture 1 Course logistics and references, physics overview.
28-Sep-2009 lecture 2 Solving the (many-body) Schrodinger equation, variational/basis wave function methods, Stochastic Variation Method (SVM).
30-Sep-2009 lecture 3 Review of thermodynamics/statistical mechanics relevant for many-body path integrals; introduction of model partition function.
05-Oct-2009 lecture 4 Symmetry factors for the model partition function.
07-Oct-2009 lecture 5 Loose ends on symmetry factors and partial resummations. Saddlepoint/steepest descent and auxiliary field manipulations for the model partition function.
12-Oct-2009 lecture 6 Introduction to the functional integral formalism, using a single-particle quantum mechanics example. Also an introduction to the stochastic evaluation of path integrals.
14-Oct-2009 lecture 7 Recap and further discussion of stochastic evaluation of path integrals and follow-ups to the one-particle path integral, leading to its generalization.
19-Oct-2009 lecture 8 Perturbation theory for the one-particle path integral, functional derivatives, intro to 2nd quantization and coherent states.
21-Oct-2009 lecture 9 Functional derivative and Feynman rule practice. 2nd quantization and field operators. Coherent states and classical harmonic oscillator.
26-Oct-2009 lecture 10 Coherent state path integral, Grassmann numbers and coherent states, dilute Fermi gas with delta function interaction, Feynman rules.
28-Oct-2009 lecture 11 Molecular dynamics and preliminary inversion strategies.
02-Nov-2009 lecture 12 Comments on PS#2; background on non-interaction fermion and boson noninteracting gases.
04-Nov-2009 lecture 13 Feynman rules recap. Results for non-interacting system. Spin-sum simplification with Mathematica. Spin-dependent force. Beachball diagram. Dyson's equation.
09-Nov-2009 lecture 14 Momentum space Feynman rules example. Beachball lead-in to effective field theory (EFT).
11-Nov-2009 lecture 15 Further discussion of hybrid Monte Carlo.
16-Nov-2009 lecture 16 Renormalization in the EFT for short-range interactions, with application to the dilute Fermi gas. Cutoff and dimensional regularization.
18-Nov-2009 lecture 17 Large nu limit of dilute Fermi gas. Start of effective action discussion.
23-Nov-2009 lecture 18 Application of effective action to large N (large nu) example.
30-Nov-2009 lecture 19 Effective action for pairing.

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Mathematica Notebooks

On some machines clicking the link will start Mathematica directly. If not, "right click" to save the file and then read it into Mathematica separately.

Date OutNotebookComments
10/15/09 Rolling Dice Mathematica notebook that simulates the rolling of dice, where the outcome is a random integer from 1 to 6. Histograms are generated for different numbers of "trials" (i.e., throws of the dice), providing visualization of how the fluctuations scale with the number of trials.
11/04/09 DeltaSimplify Mathematica package defining DeltaSimplify to simplify spin sums.
11/04/09 Spin Sums I Mathematica notebook with examples of evaluating spin sums using the simplification package (deltasimplify.m).

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*Many-Body Physics References

Especially Recommended

The call number is linked to the OSCAR entry. In some cases, this entry includes the table of contents of the book.

Author(s)TitleCall no.Comments
A. Atland and B. Simons Condensed Matter Field Theory QC173.454 .A48 2006 Recent book very much in the spirit of the RG/EFT approach to many-body physics with emphasis on low-energy field theories, path integrals, universality. More a condensed matter than particle theory outlook. Expensive!
A.L. Fetter and J.D. Walecka Quantum Theory of Many-Particle Systems QC174.5.F43 1971 Classic text, but pre-path integrals. Now available in an inexpensive (about $20) Dover reprint. Get it!
J.W. Negele and H. Orland Quantum Many-Particle Systems QC174.17.P7 N44 1988 Detailed and careful use of path integrals. Full of good physics but most of the examples are in the problems, so it can be difficult to learn from.
J. Zinn-Justin Quantum field theory and critical phenomena QC174.45 .Z56 2002 Encyclopedic, rigorous reference. Excellent on path integrals and renormalization.
N. Nagaosa Quantum Field Theory in Condensed Matter Physics QC174.45.N27 1999 Covers path integral methods and symmetry breaking.
M. Stone The Physics of Quantum Fields QC174.45.S79 2000 A combined introduction to quantum field theory as applied to particle physics problems and to nonrelativistic many-body problems. Some very nice explanations.
R.D. Mattuck A Guide to Feynman Diagrams in the Many-Body Problems QC174.5.M34 1967 This is a nice, intuitive guide to the meaning and use of Feynman diagrams. The second edition is from 1976, but the library may only have the older edition. A paperback version is available from Amazon (and probably elsewere) for under $11.
W.H. Dickhoff and D. van Neck Many-body theory exposed! : propagator description of quantum mechanics in many-body systems QC174.17.P7 D53 2008 Up-to-date propagator-based description of many-body physics. No path integrals, so complementary to our treatment in many respects.
N. Goldenfeld Lectures on Phase Transitions and the Renormalization Group QC175.16.P5 G65 1992 The discussion of scaling, dimensional analysis, and phase transitions is wonderful.
G.D. Mahan Many-Particle Physics QC176.M24 2000 Standard, encyclopedic reference.
K. Huang Statistical Mechanics QC174.8.H83 1987 Excellent choice for general treatment of statistical mechanics, with good sections on many-body physics.
J. Kohanoff Electronic structure calculations for solids and molecules : theory and computational methods QD462.6.D45 K64 2006 Good, up-to-date introductory guide to quantum chemistry methods.

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Other Useful Texts

The call number is linked to the OSCAR entry. In some cases, this entry includes the table of contents of the book.

Author(s)TitleCall no.Comments
P. Nozieres Theory of Interacting Fermi Systems QC174.5 .N651 1964 Outdated in many ways, but great physics explanations. (Three copies are available.)
J.F. Donoghue, E. Golowich, B.R. Holstein Dynamics of the Standard Model QC794.6.S75 D66 1991 Good introduction to low-energy, standard model physics.
P. Ring and P. Schuck The Nuclear Many-Body Problem QC174.17.P7 R56 1980 Somewhat out of date, but still a good, encyclopedic guide to the nuclear many-body problem. Doesn't discuss Green's function methods much and no path integrals.
P.J. Siemens and A.S. Jensen Elements of Nuclei: Many-Body Physics with the Strong Interaction QC793.3.S8 S54 1987 Good survey of nuclear phenomenology and basic methods.
Abrikosov, Gorkov and Dzyalozinskii. Methods of Quantum Field Theory in Statistical Physics QC174.4 .A21 1975 Old but classic. Referred to as "AGD".
P.W. Anderson Basic notions of condensed matter physics QC173.4.C65 A53 1984 Another classic.
A.M. Tsvelik Quantum Field Theory in Condensed Matter Physics QC174.45.T79 1995 Lots on one-dimensional systems.
E. Fradkin Field theories of condensed matter systems QC611.98.H54 F73 1991 Good reference for fractional statistics and quantum hall effect.
Y. Suzuki and K. Varga Stochastic variational approach to quantum-mechanical few-body problems QC174.17.P7 S89 1998 The bible on the SVM method. Very accessible.

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Related Review and Journal Articles

  1. P. Lepage, "How to Renormalize the Schrodinger Equation" (1997).
  2. R. Shankar, "Renormalization-group approach to interacting fermions", Rev. Mod. Phys. 66, 129 (1994).
  3. R.J. Furnstahl, G. Rupak, and T. Schafer, "Effective Field Theory and Finite-Density Systems", Annual Review of Nuclear and Particle Science 58, 1 (2008).
  4. J. Drut, R.J. Furnstahl, and L. Platter, "Toward ab initio density functional theory for nuclei", to appear in Progress in Particle and Nuclear Physics (2009).
  5. S. Aoki, T. Hatsuda, N. Ishii, "Nuclear Force from Monte Carlo Simulations of Lattice Quantum Chromodynamics" (2008).
  6. S. Weinberg, "Why the Renormalization Group is a Good Thing". Great essay!
  7. Path Integral Monte Carlo references
    1. Online notes on the path integral Monte Carlo method.
    2. More Online notes on the path integral Monte Carlo method.
    3. Open source path integral simulation program developed by the Shumway research group.
    4. D. M. Ceperley, "Path integrals in the theory of condensed helium", Rev. Mod. Phys. 67 279.
  8. W. Kohn, "Nobel Lecture: Electronic structure of matter --- wave functions and density functionals", Rev. Mod. Phys. 71 (1999) 1253.
  9. N.J. Higham, "The Scaling and Squaring Method for the Matrix Exponential Revisited", SIAM. J. Matrix Anal. & Appl. 26 (2005) 1179.

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Your comments and suggestions are appreciated.
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