Marco Lastres

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Understanding the structure of operators that commute with k identical replicas of a unitary ensemble, also known as its k-commutant, is an important problem in quantum many-body physics with deep implications for the late-time behavior of physical quantities such as correlation functions, OTOCs, and Rényi entanglement entropies under unitary evolution.

For free-fermion and interacting systems, we introduce a geometric description of k-commutants in terms of "commutant manifolds", which encode the local structure of the commutant for any system size. For free-fermion (Gaussian) models we show that these manifolds are smooth Grassmannians, while for interacting systems they generically possess singular points.

We show that the quantum geometry of these manifolds controls the evolution of observables in random circuit dynamics, yielding a direct and non-perturbative derivation of operator and entanglement hydrodynamics in these systems.

Based on arXiv:2604.05031 and arXiv:2608.11297.

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TUM
0.03
Contact: Xhek Turkeshi