COURSE TIME:
MoWe 11:00 am -12:20 pm, Roessler 158.
INSTRUCTOR 1: Richard Scalettar, scalettar@physics.ucdavis.edu
OFFICE: Physics-Geology 409.
OFFICE HOURS: We. 12:20-2:00; or by appointment.
INSTRUCTOR 2: Warren Pickett, pickett@physics.ucdavis.edu
OFFICE: Physics-Geology 427.
OFFICE HOURS: TBA
REQUIRED TEXT: None
USEFUL BOOKS:
`Condensed Matter Physics', M. Marder
'Lecture Notes on Electron Correlation and Magnetism',
P. Fazekas
GENERAL DESCRIPTION:
This course will cover quantum magnetism, both from the viewpoint of model Hamiltonians such as those of Heisenberg and Hubbard and also within the more `ab initio' density functional theory framework which is required to describe the details of real materials. Quantum magnetism is an immense field, and the background of the students might vary considerably. So this syllabus is just a starting point. At the beginning of the course we will survey the students to get an idea of whether this syllabus should be modified better to reflect the particular interests and technical expertise of those enrolled. A word too on grading. The material/problems presented here would certainly offer the student who really was intent on this topic to put in a lot of hours. We expect there will be some such students. On the other hand, we recognize that there will also be some students to whom this topic is interesting, but less central to their intended research. We intend to offer a couple of different levels of difficulty on the main projects to reflect that, and also assign grades with the understanding that there will be these differences coming in.
DETAILED DESCRIPTION/SYLLABUS:
1) Introduction (Scalettar/Pickett)What is the origin of magnetic moments in atoms and solids?
Many-Body wavefunctions, including spin
How and why do the moments interact with each other?
Magnetic coupling between atoms: hydrogen molecule and beyond
Direct exchange vs. superexchange
2) The Heisenberg Hamiltonian (Scalettar)
What is the Heisenberg Hamiltonian?
For what materials might it be an appropriate model?
Exact solution of two and four site systems.
Numerical solution: Exact diagonalization.
Spin Waves.
Quantum Monte Carlo.
3) The Hubbard Hamiltonian (Scalettar)
What is the Hubbard Hamiltonian?
What are some of the simple arguments for its basic properties?
For what materials might it be an appropriate model?
(How do we get from many bands to a single band?)
Numerical solution: Exact diagonalization.
Mean field theory of the Hubbard model.
Quantum Monte Carlo.
4) Density Functional Theory and Real Materials (Pickett)
What is density functional theory?
How is magnetism treated within density functional theory?
What are some of the detailed magnetic properties of real materials
that model Hamiltonians would not be good at looking at, but which
DFT might get better insight into?
ASSIGNMENT ONE
Spin-1/2 and Hund's Rules
ASSIGNMENT TWO
Susceptibility of Pr(3+) and Four Site Heisenberg
ASSIGNMENT THREE
Resonating Valence Bond State for Four Site Heisenberg
ASSIGNMENT FOUR
Path Integral Representation of Spin in Transverse Field, Quantum Oscillator
ASSIGNMENT FIVE
Two site Hubbard Model; MFT of Hubbard Model; Spinless Fermions in 1-d
Notes on Problem 2 of Assignment 5
MFT for Hubbard Model, Ferromagnetism
MFT for Hubbard Model, Anti-Ferromagnetism
Numerical Recipes Home Page
IMPORTANT NOTE:
PROGRAMS BELOW WHICH USE NUMERICAL RECIPES ROUTINES ARE TO BE USED ONLY FOR THE HOMEWORK PROBLEMS ASSIGNED IN CLASS! FOR OTHER USES YOU SHOULD PURCHASE A COPY OF THE NUMERICAL RECIPES BOOK.
FILE FOR INVERTER IN FORTRAN:
invert2.f
FILE FOR DIAGONALIZER IN FORTRAN:
diag2.f
FILES FOR DIAGONALIZER IN C:
Notes on compilation and use
jacobi.c
nrutil.c
nrutil.h
jacobi_test.c
input.txt
FILE FOR INVERTER IN C:
invert2.c
FILES FOR RANDOM NUMBER GENERATOR IN FORTRAN:
ran2.f
FILES FOR RANDOM NUMBER GENERATOR IN C:
Notes on compilation and use
r1279.c
r1279.h
test.c