Proseminar: Theory of Quantum Matter

Michael Knap, Johannes Knolle, Frank Pollmann

First Meeting: 
Nov. 3, 14:00 - 15:00

The seminar will be offered this semester at the announced times and will be based on Zoom. Further details will be sent by email to all participants registered in campus online. Please sign up online to be able to receive the latest information.

List of presentations:

Spin liquids and topological phases

Monopoles in spin ice
THY: Magnetic monopoles in spin ice, C. Castelnovo, R. Moessner, S. L. Sondhi, Nature 451, 42-45 (2008).
EXP: Spin Ice State in Frustrated Magnetic Pyrochlore Materials, Steven T. Bramwell and Michel J. P. Gingras, Science, 294, 1495-1501 (2001).

Quantum Dimer Models 
THY: Superconductivity and the quantum hard-core dimer gas, D. S. Rokhsar, S. A. Kivelson, Physical Review Letters 61 (20), 2376 (1988).

Toric Code and fault-tolerant quantum computation 
THY: Fault-tolerant quantum computation by anyons, A. Yu. Kitaev, Annals Phys. 303 (2003) 2-30 (2003), (Ch. 1, Ch 2.1, Ch 2.2).

Topological order in a 3D toric code at finite temperature
THY: Claudio Castelnovo and Claudio Chamon, Phys. Rev. B 78, 155120 (2008).

Berezinskii–Kosterlitz–Thouless transition in two dimensions 
EXP: Rémi Desbuquois, Lauriane Chomaz, Tarik Yefsah, Julian Léonard, Jérôme Beugnon, Christof Weitenberg, Jean Dalibard, Superfluid behaviour of a two-dimensional Bose gas, Nature Physics 8, 645 (2012).
THY: J. M. Kosterlitz and D. J. Thouless, J. Phys. C: Solid State Physics 6, 1181 (1973), Statistical Physics of Particles: Mehran Kardar

Topological band structures
THY: Haldane, F. D. M. Model for a quantum Hall Effect without Landau levels: condensed-matter realization of the ‘parity’ anomaly. Phys. Rev. Lett. 61, 2015 (1988)
EXP: Experimental realization of the topological Haldane model with ultracold fermions Gregor Jotzu, Michael Messer, Rémi Desbuquois, Martin Lebrat, Thomas Uehlinger, Daniel Greif & Tilman Esslinger Nature 515,  237 (2014)

Harper–Hofstadter model
EXP: M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch Phys. Rev. Lett. 111, 18530 (2013).
THY: Douglas R. Hofstadter Phys. Rev. B 14, 2239 (1976).

Determine topology of Bloch bands 
EXP: Lucia Duca, et al, An Aharonov-Bohm interferometer for determining Bloch band topology, Science 347, 288 (2015). 
THY: Dmitry A. Abanin, et al. Interferometric Approach to Measuring Band Topology in 2D Optical Lattices, Phys. Rev. Lett. 110, (2013).

Quantum matter out of equilibrium

Anderson's Orthogonality Catastrophe 
THY: P. W. Anderson, Infrared Catastrophe in Fermi Gases with Local Scattering Potentials, Phys. Rev. Lett. 18, 1049 (1967). 
EXP: M. Cetina, et al, Ultrafast many-body interferometry of impurities coupled to a Fermi sea., Science 354, 96 (2016).

Anderson Localization 
THY: Anderson, P. W. Absence of diffusion in certain random lattices. Physical Review 109, 1492–1505 (1958). EXP: Billy, J. et al. Direct observation of anderson localization of matter waves in a controlled disorder. Nature 453, 891–894 (2008).

Eigenstate thermalization 
THY: Thermalization and its mechanism for generic isolated quantum systems, Marcos Rigol, Vanja Dunjko, Maxim Olshanii Nature 452 854 (2009). 
EXP: A quantum Newton's cradle, Toshiya Kinoshita, Trevor Wenger and David S. Weiss Nature 440, 900 (2006).

Many-body localization 
THY: Arijeet Pal, David A. Huse, The many-body localization phase transition, Phys. Rev. B 82, 174411 (2010), arXiv:1010.1992.
THY: Jens Bardarson, et al. Unbounded growth of entanglement in models of many-body localization, Phys. Rev. Lett. 109, 017202 (2012), arXiv:1202.5532.
EXP: Michael Schreiber, et al. Observation of many-body localization of interacting fermions in a quasi-random optical lattice, Science 349, 842 (2015), arXiv:1501.05661.

Periodically driven many-body systems
THY: Photovoltaic Hall effect in graphene, T Oka, H Aoki Physical Review B 79, 081406 (2009). 
EXP: Observation of Floquet-Bloch states on the surface of a topological insulator, YH Wang, H Steinberg, P Jarillo-Herrero, N Gedik Science 342, 453 (2013).

Time crystals 
THY: Floquet Time Crystals, Dominic V. Else, Bela Bauer, and Chetan Nayak, Phys. Rev. Lett. 117, 090402 (2016). 
EXP: Observation of discrete time-crystalline order in a disordered dipolar many-body system, Soonwon Choi, et al. Nature 543, 221 (2017).

Dynamical Quantum Phase transitions 
THY: Dynamical Quantum Phase Transitions in the Transverse Field Ising Model, Markus Heyl, Anatoli Polkovnikov, Stefan Kehrein Phys. Rev. Lett. 110, 135704 (2013), Dynamical quantum phase transitions: A brief survey, Markus Heyl, 
EXP: Direct observation of dynamical quantum phase transitions in an interacting many-body system, P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, C. F. Roos, Phys. Rev. Lett. 119, 080501 (2017), arXiv:1612.06902.

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