Discrete toy models

Discrete quantum systems, such as infinite spin chains or other many-body systems, have a storied history in condensed matter theory. Such systems serve as good testbeds for ideas in quantum information theory involving multiple parties. Those interested in holography sometimes use them as toy models to better understand gravitational phenomenon from the quantum, nongravitational side of the holographic correspondence. Additionally, certain classes of discrete quantum-error-correcting codes have even been studied as toy models of holographic duality itself.

My interest in discrete toy models is motivated by my interest in holography. Specifically, I use such systems to better understand ideas that are known to be of great importance in AdS/CFT. These ideas include complexity, which measures how "hard" it is to prepare a particular quantum state, and quantum chaos, i.e. the quantization of highly sensitive dynamical systems and their evolution in time. Such concepts are believed to encode aspects of black hole physics. While they are notoriously tricky to define and describe in continuum QFT, doing so in discrete quantum systems is more tractable.

I am also interested in using these types of systems to understand the holographic emergence of spacetime. This has ramifications for what holography "means" and is pivotal to understanding how to apply it beyond the realm of AdS gravity.

Selected publications

Y. Fan, J. Couch, SS, Circuit Complexity in Topological Quantum Field Theories. Fortschritte der Physik 70 (2022) 9–10, 2200102. arXiv:2108.13427, preprint Aug 2021.

Under review

B. Kent, S. Racz, SS, Scrambling in quantum cellular automata. Under review by Physical Review B. arXiv:2301.07722, Jan 2023.

Work in progress

SS, HaPPY holographic renormalization group flow.