Balázs Pozsgay (ELTE Dept. of Theoretical Physics)

Dual unitary circuits: solvable models of quantum chaos

Abstract: We give an introduction into a topic which is a new research direction for our group (MTA-ELTE Momentum Integrable Quantum Dynamics Group). The dual unitary circuits are one dimensional quantum block cellular automata, where the fundamental two-site gate satisfies a special mathematical condition, the dual unitarity (sometimes also called biunitarity). This condition can be understood as a sort of space-time duality: the circuit is unitary also when we exchange the role of time and space. Eventually this leads to their solvability: dynamical correlation functions can be computed exactly. Even though these circuits are rather special (not generic), one can argue that they display many key properties of quantum chaos. Furthermore, in some cases the circuits are integrable (in the usual sense, having many conserved charges, etc). We discuss the dynamical properties of these circuits, and also relations with other subjects/topics such as holographic error correcting codes, combinatorial designs, and Yang-Baxter integrability.

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