Course Announcement 8820 Computational Many Body Theory for Spring Semester 2015

[Nandini Trivedi]

*8820    ‘Special Topics – Computational Many Body Theory’ *

*Nandini Trivedi [class #27158]*

*Spring Semester 2015  January 12- April 27 WF 3:00-4:20 *



*Approach and Philosophy:*

My aim in this course is to give an integrated view of Interacting Models,
Experiments and Theoretical Methods. The students will not be by-standers
listening to me but will be active participants throughout the course.



*Content of Course:*

Part A:

I will start with the Hubbard model and its exact solution for few sites. I
will then discuss specific correlation functions or dynamical
susceptibilities measured in various experiments: photoemission, neutron,
Raman, NMR and compare these with explicit calculations of the few-site
Hubbard model.



To understand each experimental technique, my general principle will be to
check

(1) “anchor points” – behavior in limiting cases such as free electrons,
free bosons, free spins

(2) Sum rules



Part B:

I will apply different theoretical techniques on the Hubbard Model and
critique their advantages and disadvantages. Among these techniques will be
(a) perturbation theory at weak coupling and strong coupling; (b) mean
field theory; (c) variational theory; (d) path integral methods.



*Pre-requisites:*

(1) Core Courses

(2) Condensed Matter Physics

(3) Basic Computational Physics [At the level of ipython, mathematica or
matlab]

If you do not have all the pre-requisites please e-mail me so we can
discuss further.



*Structure of Course:*

There will be 2 lectures per week: In addition to my lectures there will be
extensive class discussion and presentations by students of homeworks
throughout the course.

This will form the basis of the grade. There will be no other project or
exams.



*Timeline:*

PART A:

Week 1: Hubbard Model, introduction, key papers

Week 2-6: Comparisons between

Exact diagonalization; Calculation of thermodynamics, equal time
correlation functions, spectroscopies and experiments



PART B:

Week 7: Strong coupling perturbation theory in t/U around Mott state ;
origin of Heisenberg magnetism

Week 8: Transverse Field Ising model: weak and strong coupling expansions;

Week 9: Mean field theory

Week 10-11: Variational method; Monte Carlo

Week 12-13: Path integral methods; auxiliary field methods

Week 14: Recap; Open Problems

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***********************
Nandini Trivedi
Professor
Department of Physics
The Ohio State University
191 W. Woodruff Avenue
Columbus, OH 43210
t: (614) 247 7327
f: (614) 292 7557
e: trivedi.15 at osu.edu
w: http://www.physics.ohio-state.edu/~trivedi/
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