Title: Partition Function of the Sachdev-Ye-Kitaev Quantum Mean Field Model
Abstract: The Sachdev-Ye-Kitaev (SYK) is a quantum mean-field model studied in condensed matter physics, physics of black holes and theoretical computer science. Its structural properties were derived heuristically in physics using a combination of the replica method and path integration techniques. Analyzing it mathematically rigorously in proper probabilistic framework, however, turned out to be notoriously difficult. In this paper we rigorously compute the partition function for this model at high enough but constant temperature. Our results are in numerical agreement with the results derived by physics methods. The method of proof is novel and is different from the physics approach. It is based on the theory of the component structure of sparse random graphs and large deviations techniques. It provides another intriguing example how physics heuristics methods, such as path integration and replica method, can be validated mathematically, albeit using different techniques.
The talk will be self-contained and require no background in quantum computing.
Joint work with Francisco Pernice (MIT), Alexander Schmidhuber (MIT), Alexander Zlokapa (MIT)
3:30pm - Pre-talk meet and greet teatime - 219 Prospect Street, 13th floor, there will be light snacks and beverages in the kitchen area.
