Modul physik7507

SS 2020

Quantum Magnetism

The information about this course is hosted on eCampus. This page will just mirror the information given there.

If you have questions concerning the lecture, contact us or pass by the office room 1.032b, PI.

About the Lecture

This lecture will introduce you to the quantum theory of magnetism.

The lecture takes place on Thursdays from 10 to 12 in the room: Konferenzraum I, W 0.027, PI.
Due to the coronavirus pandemic, this semester starts with digital teaching. For more information on how to participate in the online lecture, visit the eCampus page.

The first exam is going to take place on the 28.07.2020 from 9 to 11 in the lecture hall of the HISKP.

Literature

We will follow:

P. W. Anderson, Basic Notions of Condensed Matter Physics (1984).
A. Auerbach, Interacting Electrons and Quantum Magnetism (1994).
Yu. A. Izyumov, and Yu. N. Skryabin, Statistical Mechanics of Magnetically Ordered Systems (1988).
C. Kittel, Quantum Theory of Solids (1963).

Additionally, we encourage the students to read the following articles:

P. W. Anderson, New Approach to the Theory of Superexchange Interactions, Phys. Rev. 115 (1959) 2,
URL: https://journals.aps.org/pr/abstract/10.1103/PhysRev.115.2
B. N. Brockhouse, and H. Watanabe, Spin Waves in Magnetite from Neutron Scattering (1962),
URL: https://www.osti.gov/biblio/4763367
S. Chakravarty, B. I. Halperin, and D. R. Nelson, Two-Dimensional Quantum Heisenberg Antiferromagnet at low Temperatures, Phys. Rev. B 39 (1989) 2344,
URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.39.2344
M. Arai, M. Fujita, M. Motokawa, J. Akimitsu, and S. M. Bennington, Quantum Spin Excitations in the Spin-Peierls System CuGeO₃, Phys. Rev. Lett. 77 (1996) 3649,
URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.77.3649
A. J. Millis, and H. Monien, Spin gaps and bilayer coupling in YBa₂Cu₃O_7-δ and YBa₂Cu₄O₈, Phys. Rev. B 50 (1994) 16606,
URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.50.16606
L. Balents, Spin liquids in frustrated magnets, Nature 464 (2010) 199,
URL: https://www.nature.com/articles/nature08917
M. V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. Lond. A 392 (1984) 45,
URL: https://royalsocietypublishing.org/doi/10.1098/rspa.1984.0023
I. Affleck, Quantum spin chains and the Haldane gap, J. Phys.: Condens. Matter 1 (1989) 3047,
URL: https://iopscience.iop.org/article/10.1088/0953-8984/1/19/001
L. P. Kadanoff, Scaling laws for ising models near T_c, Physics Physique Fizika 2 (1966) 263,
URL: https://journals.aps.org/ppf/abstract/10.1103/PhysicsPhysiqueFizika.2.263
J. M. Kosterlitz, and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C: Solid State Phys. 6 (1973) 1181,
URL: https://iopscience.iop.org/article/10.1088/0022-3719/6/7/010
V. L. Berezinsky, Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group. I. Classical systems, Sov. Phys. JETP 32 (1971) 493,
URL: https://inspirehep.net/literature/61186
H. Bethe, Zur Theorie der Metalle, Z. Physik 71 (1931) 205,
URL: https://link.springer.com/article/10.1007/BF01341708
J. des Cloizeaux, and J. J. Pearson, Spin-Wave Spectrum of the Antiferromagnetic Linear Chain, Phys. Rev. 128 (1962) 2131,
URL: https://journals.aps.org/pr/abstract/10.1103/PhysRev.128.2131
C. N. Yang, and C. P. Yang, One-Dimensional Chain of Anisotropic Spin-Spin Interactions. I. Proof of Bethe's Hypothesis for Ground State in a Finite System, Phys. Rev. 150 (1966) 321,
URL: https://journals.aps.org/pr/abstract/10.1103/PhysRev.150.321
N. Andrei, K. Furuya, and J. H. Lowenstein, Solution of the Kondo problem, Rev. Mod. Phys. 55 (1983) 331,
URL: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.55.331

Exercises

The tutorial takes place on Tuesdays from 11 to 12 o'clock in the room: Ü2, Raum 0.033, AVZ I.

Please hand in your solutions until Mondays 14 o'clock in front of the room 1.032 in the PI.
As long as the semester is carried out digitally, send your solutions via e-mail to hoellmer@physik.uni-bonn.de.

In order to attend the final examination, the students need to attain at least 50% of the points on the exercise sheets.

Exercise sheet 01 (due date: May 04)
Exercise sheet 02 (due date: May 11)
Exercise sheet 03 (due date: May 18)
Exercise sheet 04 (due date: May 25)
Exercise sheet 05 (due date: June 01)
Exercise sheet 06 (due date: June 08)
Exercise sheet 07 (due date: June 15)
Exercise sheet 08 (due date: June 22)
Exercise sheet 09 (due date: June 29)
Exercise sheet 10 (due date: July 06)
Exercise sheet 11 (due date: July 13)