Course Announcements:

• 6/18: All grades have been submitted to the registrar. It's been a fun quarter: enjoy the summer!

Course Information:

Instructor: Sid Parameswaran, Assistant Professor

310J Rowland Hall, sidp_at_uci.edu

Lectures: Tuesday/Thursday 2:00PM - 3:20 PM, PSCB230.

Office Hours: Tuesdays, 3.30-4.30PM, Rowland 310J.

Overview:

This is the last in a three-course graduate sequence on condensed matter physics. Historically, this course has focused on traditional topics such as superconductivity and magnetism. While the physics I discuss is ultimately of deep relevance to modern problems in both these fields, I will take a rather different perspective than in past iterations.

This course will be aimed at graduate students interested in modern condensed matter theory and high energy physics. Primarily, we will be concerned with using the tools of quantum field theory to understand a wide variety of quantum systems.

Our focus will be on field theories that naturally emerge from lattice models: these are therefore effective theories, that come naturally with a lattice-scale cutoff; as such, they are regulated QFTs. Using these tools, we will cover some of the basic ideas upon which our picture of a variety of complex and strongly interacting quantum systems is built. Our approach will be to solve canonical "model systems"; thanks to the powerful ideas of renormalization, these models distill the essential properties of particular phases of matter, and yet are simple enough to understand (quasi-) analytically.

The specific topics to be covered will vary depending on the composition of the class and student interest, but a tentative list includes: quantum-classical correspondence; quantum phase transitions; dualities; lattice gauge theories and deconfinement; instanton effects in quantum theories; spontaneous symmetry breaking; the Bose-Hubbard model and superfluid-insulator transitions; the large-N approximation; 1+1D systems, with a particular focus on the Kosterlitz-Thouless phase transition; characterizing quantum phases through entanglement; the basic physics of the fractional quantum Hall effect and topological order.

Prerequisites:

The prior two courses in this sequence are useful, but not essential, preparation; their primary utility is to familiarize you with working on-lattice. Familiarity with field theory, while not required, is also a bonus - particularly, an acquaintance with the language of second quantization will be rather useful. I will expect familiarity with quantum mechanics and statistical mechanics at the level of our own first-year courses.

Textbook(s):

There is no single textbook that covers the material in this course; I will suggest various references as the quarter progresses, but here is a list of potentially useful books and monographs.

• Quantum Phase Transitions, Subir Sachdev, 2nd Ed, Cambridge University Press.
• Gauge Fields and Strings, Alexander Polyakov, Harwood Academic Publishers.
• Quantum Field Theory of Many-Body Systems, Xiao-Gang Wen, Oxford University Press.
• Field Theories of Condensed Matter Physics, Eduardo Fradkin, 2nd Ed, Cambridge University Press.
• Scaling and Renormalization in Statistical Physics, John Cardy, Cambridge University Press.
• Condensed Matter Field Theory, 2nd Ed, Alexander Altland and Ben Simons, Cambridge University Press.
• Statistical Physics of Fields, Mehran Kardar, Cambridge University Press.

In addition, I may post or suggest advanced reading from other books or journal articles.

Lecture Notes and Course Outline:

While I will link to lecture notes, I suggest that you take notes in class - particularly as this is an advanced course, I hope there will be a fair amount of discussion in 'real time' that you might like to have a record of.

Here is the full set of lectures (PDF link, frequently updated file).

Problem Sets:

There will be 4-5 problem sets posted intermittently through the quarter.

1. Problem Set 1, due Thursday, April 23, 2015.
2. Problem Set 2, due Thursday, May 7, 2015.
3. Problem Set 3, due Thursday, May 21, 2015.
4. Problem Set 4, due Thursday, June 4, 2015.
5. Problem Set 5, due Thursday, June 11, 2015.

Solutions in PDF form available on request - please email me directly if you require these.

Grading:

Your grade will be based on the problem sets (80%) and class participation (20%). (Note that this represents a change from the original grading scheme, based on a unanimous vote taken in class to drop the final project in favor of more homeworks.)