__ 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

### ASSIGNMENT TWO

### ASSIGNMENT THREE

### ASSIGNMENT FOUR

### ASSIGNMENT FIVE

### 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:

### FILE FOR DIAGONALIZER IN FORTRAN:

### FILES FOR DIAGONALIZER IN C:

### FILE FOR INVERTER IN C:

### FILES FOR RANDOM NUMBER GENERATOR IN FORTRAN:

### FILES FOR RANDOM NUMBER GENERATOR IN C: