Eigenstate Thermalization in Dual Unitary Quantum Circuits

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The successful description of isolated quantum systems by thermodynamic equilibrium states has triggered the question how those systems thermalize from a typical pure initial state under unitary time evolution. The eigenstate thermalization hypothesis (ETH) conjectures an answer in terms of a mathematical ansatz which describes the structure of matrix elements of macroscopic observables. Although numerical studies provide strong evidence for ETH in generic many-body quantum systems, analytical proofs that a given system indeed fulfills ETH are rare. In this project I propose to study eigenstate thermalization in dual-unitary quantum circuits and to rigorously confirm ETH and its implications. Such quantum circuits provide minimal models for generic many-body quantum systems and allow for an analytical description of their prominent features. In particular dual-unitary circuit models, which exhibit an additional space-time symmetry, are suitable for exact calculations and thus are excellent candidates for an analytic confirmation of ETH. To this end I plan to (i) numerically investigate eigenstate thermalization in dual-unitary quantum circuits, (ii) establish an analytical description of their quantum dynamics, (iii) confirm the ETH ansatz for local observables, (iv) study entanglement properties of eigenstates, and (v) extend the properties of dual-unitary quantum circuits to more generic many-body systems.