**Physics 223B, Graduate Condensed Matter Physics, Winter 2015**

**Prof. Matthew Fisher **

email: mpaf@kitp.ucsb.edu ;

Office: 2305 Kohn Hall

Lectures: Monday, Wednesday 9:30-10:45 am, Phelps 2514

Office Hours: Monday 2:00-3:00, Tuesday 3:00-4:00 pm

Find the course web site thru my personal web site: http://www.kitp.ucsb.edu/mpaf

**Grader/TA: Jennifer Cano**

email: jcano@physics.ucsb.edu ;

Office: Elings Hall, 2nd Floor, Northeast corner

Office Hours: Thursday 3-4pm, Friday 2-3pm

**Condensed Matter Physics: **Condensed matter physics is an enormously broad field, arguably "larger" than all of the other subfields of physics combined. Even in a full year sequence it is impossible to even touch upon the myriad of phenomena. To complement 223A, in 223B I will try to focus on **collective (i.e. emergent) phenomena**, in which the whole is more than the sum of the parts. Important concepts will include symmetry breaking, order parameters, collective excitations and other. My intention is to focus predominantly on 3 broad areas, (i) Quantum Magnetism of Insulating Crystals, (ii) Superfluidity in Many-Boson systems (e.g. 4-He) and (iii) Superconductivity phenomenology plus BCS theory - time permitting. See a tentative syllabus below, subject to change.

**Textbooks**: No official text book, since I will not follow any one book. On magnetism, some books are (i) Ashcroft and Mermin, (ii) Interacting Electrons and quantum magnetism by A. Auerbach, and (iii) Electron Correlations and Magnetism by P. Fazekas. Nice books on superfluidity are (i) Statistical Physics by Feynmann and (ii) Statistical Mechanics by Landau and Lifshitz. The book by Tinkham, Introduction to Siperconductivity, is quite accessible, and fairly complete.

**Homework**: Roughly 5-6 homeworks throughout the quarter, available on the course web site. Homework solutions also posted online. You are encouraged to work together on the homeworks.

**Exams**: Perhaps last homework as a Take-Home final.

**Help/feedback**: In addition to my office hours and Jen's office hours, I would be happy to schedule a mutually convenient time to chat about homework or other topics (best arranged by e-mail). I would greatly appreciate feedback on any aspect of the course, anytime throughout the quarter.

**SYLLABUS: (tentative)**

**Magnetism of Insulating Crystals:**

- Single atoms/ion, Hunds rules, intraatomic exchange
- Magnetic interactions, interatomic exchange, Heisenberg model, ring exchange
- Collective Magnetic Phenomena overview: magnetic ordering, symmetry breaking, valence bond crystals, spin liquids, experimental probes
- Ferromagnetism; Ground states, spin-wave theory, mean-field theory of ordering, domain walls and hysteresis
- Antiferromagnetism; Ground states, spin-wave theory for magnons, expermental probes, NMR, neutron scattering
- Other quantum states (?); Valence Bond crystals, spin liquids, topological ordering

**Superfluidity of Bosons (4-He, cold atoms):**

- Experimental Phenomenology
- Ideal Bose gas revisited
- Weakly Interacting Bosons; sound mode, condensation supression,...
- Superfluid density, quantized vortices,
- 1d (?) and 2d superfluids

**Superconductivity:**

- Experimental Phenomenology; Meissner effect, Type I, Type II, ...
- BCS Theory; ground states, excitations, thermodynamics
- Ginzburg-Landau theory

**Homework Assignments**

**Homework Solutions**