Details of PH5104 (Autumn 2012)

Level: 5 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
PH5104 Quantum Magnetism Chiranjib Mitra

Syllabus
Introduction: Origin of magnetic moments in atoms and solids. Many-Body wavefunctions, including spin. Exchange interaction. Magnetic coupling between atoms: hydrogen molecule and beyond. Direct exchange vs. superexchange. Strong correlations. Itinerant electron magnetism, Stoners criterion.



Some mathematical techniques: second quantization, correlation function calculation, many body Greens function, path integral approach, coherent state path integral, Linear Response Theory.



Transverse Field Ising model, Heisenberg Hamiltonian, low dimensional magnetic materials, spin chain etc. Some simple examples where these models are manifested. Exact solution of two and four site systems. Numerical solution: Exact diagonalization. Holstein-Primakoff representation, Spin Waves. Ghosh Majumdar Hamiltonian, Sastry Sutherland model, AKLT model and their complex ground state solutions.

The Hubbard Hamiltonian, some simple arguments for its basic properties. Variants of the Hubbard model. Some materials for which it be an appropriate model (Manganites, Nickelates, Cuprates). Numerical solution: Exact diagonalization. Mean field theory of the Hubbard model. Extension to t-j model.

Molecular Magnets. Macroscopic quantum tunneling. Tunneling of magnetization in a molecular magnet. Analogy to Josephson junctions, SQUID.

Magnetism in Metals: Strongly correlated electron systems, formation of local moments in metals. Andersons s-d interaction model, RKKY interaction. Kondo effect, Heavy Fermions and mixed valence systems, non-Fermi liquid like behaviour.

Quantum Phase Transitions in One and Two dimensional systems. Quantum criticality. Phase diagram of High Temperature Superconductors, with special emphasis on undoped Cuprates. Exotic properties of Ruthenates.

Field Theoretical methods in Quantum Magnetism. Path integral for spin systems, Effective action for Antiferromagnetic spin chains. Non-linear Sigma model and Haldanes conjecture, Antiferromagnetic spin ladders, Chains with alternating bonds, two dimensional Heisenberg Antiferromagnet, Hubbard-Stratonovich transformation, Bosonization in 1D systems.





References

  1. A. Auerbach, Interacting Electrons and Quantum Magnetism, Springer (1994)

  2. S. Sachdev, Quantum Phase Transitions, Cambridge University Press (2000)

  3. U. Schwollock, J. Richter, D.J.J Farnell and R.F. Bishop, Quantum Magnetism, Springer (2004)





Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Not Allowed
3 MS 9 Not Allowed
4 RS 1 Not Allowed