Results and new perspectives on quantum spin glasses
Professor Simone Warzel, Technical University of Munich, Germany
Quantum spin glass models of mean-field type are prototypes of quantum systems exhibiting phase transitions related to the spread of the eigenstates in configuration space. Originally motivated by spin glass physics and as complex model systems to test quantum adiabatic algorithms, they are also discussed in relation to many-body localisation phenomena. Remarkably, despite being non-integrable quantum spin glasses are expected to possess intermediate phases in which eigenstates occupy only a fraction of configuration space.
In this talk, Professor Warzel will introduce a class of hierarchical quantum glasses for which this assertion can be proven at least on the level of the specific free energy. This class constitues the quantum version of Derrida's generalised random energy models. The quantum nature is thereby incooperated through a transversal magnetic field. By proving a quantum Parisi formula for their free energy the full phase diagram is established: the model exhibits spin glass phases as well as mixed and quantum paramegnetic phases.
The mechanism behind this is the principle of erasure of hierarchical spin glass order: types of spins decide in groups whether to freeze into quantum paramagnetic order or not depending on the strength of the transversal magnetic field and the temperature.
I will conclude the talk with an overview of conjectures related to the fate of Parisi's order parameter and the structure of the eigenfunctions for these models.
Spectral statistics of chaotic many-body systems
Dr Sebastian Müller, University of Bristol, UK
We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross–Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose–Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties. (Joint work with Rémy Dubertrand)
Presentation by Steven Zelditch: talk title to be confirmed
Steve Zelditch, Northwestern University, USA
Panel Discussion 2
Professor Tomaz Prosen, University of Ljubljana, Slovenia
Professor Paul Fendley, Oxford University, UK
Professor Ehud Altman, University of California Berkeley, USA
Professor Andrew G Green, University College London, UK