Fall 2020: Special Topics in Physics (PHYS 7687)
Strongly correlated phases of quantum matter
Prerequisites: Graduate level quantum mechanics and graduate level statistical mechanics. A prior course in solid-state physics is helpful, but not required. Undergraduate students are welcome to register for the course, after discussing with the instructor.
Overview: This is an advanced graduate level course that will introduce and demystify field theory and path-integral based methods for studying quantum many-body systems. We will connect to the latest experimental developments in the field of quantum materials at every stage of the course. The aim of this course is to enable students to develop technical and intuitive skills for solving many-body problems. The course is meant for condensed matter theorists and experimentalists, as well as students from other areas of physics who want an exposure to the field.
L1 (09/02): What is this course about? Concept of quantum entanglement, universality and emergence in ultra quantum matter.
L2 (09/07): Review of free Fermi gas and Sommerfeld expansion. Introduction to Fermi liquid theory and "Landau" quasiparticles. Luttinger's theorem and its violation in (underdoped) high Tc cuprates.
L3 (09/09): Fermi liquid (FL) single-particle lifetime. Landau functional and thermodynamics of FL.
L4 (09/14): Thermodynamics of FL (contd.) and Boltzmann equation in collisionless limit.
L5 (09/16): FL collective modes: zero sound and Landau damping. Introduction to electron Green's function in a FL.
L6 (09/21): FL instability - Cooper problem. Introduction to superconductivity (SC).
L7 (09/23): London equations. Variational approach to BCS problem and mean-field theory.
L8 (09/28): BCS mean-field theory and Bogoliubov quasiparticles. Thermodynamics of a SC.
L9 (09/30): Condensation energy of BCS SC. Landau-Ginzburg theory and coherence length of a SC.
L10 (10/05): Landau-Ginzburg theory (contd.), Type-I vs. type-II SC. The "Tolmachev" logarithm and retardation. Introduction to weakly interacting Bose gas and superfluidity.
L11 (10/07): Bose-Hubbard model at strong coupling.
L12 (10/12): Bose-Hubbard model (contd.): T=0 phase diagram, Superfluid-Mott transition in ultracold atomic gases. Introduction to coherent state path integral.
L13 (10/19): Applications of coherent state path integral: Collective modes of weakly-interacting Bose gas, and, Superfluid-Mott insulator transition in Bose-Hubbard model.
L14 (10/21): Electronic Hubbard model at half-filling and strong-coupling. Super-exchange and origin of local moments. Holstein-Primakoff transformation for ordered quantum antiferromagnets.
L15 (10/26): Spin-waves in ordered antiferromagnets and ferromagnets. Effects of fluctuations. Quantum phase transitions out of long-range ordered antiferromagnets into dimerized phases.
L16 (10/28): Introduction to Z2 quantum spin liquids. Kitaev's Toric code model.
L17 (11/02): Toric code (contd.): Anyons, Topological order and ground state degeneracies. Quantum Ising model and introduction to dualities.
L18 (11/09): Z2 gauge theories: Confinement-deconfinement transition.
L19 (11/11): Emergent compact U(1) gauge theory in a frustrated Bose-Hubbard model.
(11/16 - 11/29): NO CLASSES
L20 (11/30): From Anderson impurity model to "sd" Hamiltonian. RKKY interaction b/w local moments coupled to itinerant electrons.
L21 (12/02): Kondo effect for single impurity in a Fermi sea. Poor man's scaling and flow equations for Kondo coupling.
L22 (12/07): Kondo lattice model. Introduction to "parton" (Abrikosov fermion) representation for spins.
L23 (12/09): Heavy Fermi liquid within renormalized mean-field theory. Kondo decoupling phase transition. Luttinger's theorem for "large" Fermi surface.
L24 (12/14): Introduction to non-Fermi liquid ("Strange") metals. What are the key theoretical questions?
L25 (12/16): Overview of few distinct classes of non-Fermi liquid behavior: (i) Hertz-Millis criticality, (ii) Critical Fermi surface near a continuous metal-insulator transition, and (iii) Lattices of Sachdev-Ye-Kitaev model.