Analytic studies on the SYK models: from instantaneous thermalization to holographic duality

by Jan Louw
Doctoral thesis
Date of Examination:2023-06-23
Date of issue:2023-07-18
Advisor:Prof. Dr. Stefan Kehrein
Referee:Prof. Dr. Fabian Heidrich-Meisner
Referee:Prof. Dr. Peter Sollich
Persistent Address: http://dx.doi.org/10.53846/goediss-10017

 

 

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Abstract

English

The quasiparticle picture is so prominent in condensed matter physics that it is almost taken as an axiom. Without this simplification, the physics becomes nearly intractable. However, the physics also becomes remarkable, leading to holographic connections to gravity found in such strange metals lacking a quasiparticle description. In this thesis we present analytic, i.e., mathematical results on the fermionic charged Sachdev-Ye-Kitaev (cSYK) models which capture these interesting features. We provide results on fast thermalization, chaotic-to-regular phase transitions, and charge dynamics in a lattice of such models. We also provide a concrete holographic mapping onto gravity showing how the partition functions of both charged dilaton gravity and the complex SYK model overlap exactly.
Keywords: Strongly correlated matter; holography; many body quantum systems; condensed matter; chaotic systems; general relativity; gravity
 
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