Exploring quantum chaos and its transition into the many-body regime is becoming an increasingly profound area of study. In this thesis, we focus on the transition from single-particle to many-body quantum chaos through the control of interaction strength between particles in the Sachdev-Ye-Kitaev model. This model plays a crucial role in analyzing quantum chaos, thermalization, and other areas of quantum physics.
We investigate the dependence of interaction strength through various indicators of many-body chaos commonly utilized in interacting quantum mechanics. Among these are the level spacing ratio, entanglement entropy, spectral form factor, and informational entropy. For accessible system sizes, these indicators suggest a smooth transition from single-particle to many-body chaos, indicating an exponential dependence of the critical interaction value on system size.
During the analysis of the connected spectral form factor, we examine the universal \textit{ramp} region for both many-body and single-particle systems. For the many-body Thouless time obtained from the connected spectral form factor, we observe scaling as $t_{Th}\propto \lambda^{-2.4}$.
Based on these results, we conclude that many-body chaos emerges in the thermodynamic limit for any nonzero interaction. In the limit of no interactions, the model simplifies from a many-body problem to a single-particle one, reducing the size of the Hilbert space. The non-interacting model enables the analysis of much larger physical systems through the spectral form factor, that we expressed in terms of single-particle energies.
|
