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:

11-Dec-2009 --- Some hints for PS#4 problem 2(b) are available.
07-Dec-2009 --- Some notes relevant for the final problem set on computing observables on the lattice are available.
02-Dec-2009 --- The nineteenth set of lecture notes are available.
01-Dec-2009 --- Problem Set #4 is linked below.
24-Nov-2009 --- *** Typo alert! *** Two zeta's were missing in equation (2) of PS#3 (thanks to Ken Patton for spotting this). You need them to get the matrix correct! A corrected version (with the other typo's fixed) is linked below.
18-Oct-2009 --- Some notes from the 780 Computational Physics course on Monte Carlo methods are linked under Supplementary Reading.
13-Oct-2009 --- Solving the many-particle Schrodinger equation: Take a look at the beginning of Walter Kohn's Nobel Lecture for what he says about the "exponential wall".
08-Sep-2009 --- The website from a past version (from 2003) of Physics 880.05 is still available (ask about the username/password to look at the old lecture notes). The present course will be only one quarter and is not a repeat of the first quarter of the 2003 version.

Course description and info
Assignments
- Reading due dates
- Assigned problems, hints, and solutions
General handouts
Resources

Assignments

Background or Supplementary Readings

Reading	Topic	Reading 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)	Assignment	Comments	Solutions
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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Handouts

PDF Copies of Handouts

Date Out	Handout	Comments
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 Out	Handout	Comments
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 Date	Notes	Comments
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 Out	Notebook	Comments
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)	Title	Call 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)	Title	Call 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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