Tangent space generators of matrix product states and exact floquet quantum scars Ljubotina, Marko ; https://orcid.org/0000-0003-0038-7068 Petrova, Elena Schuch, Norbert Serbyn, Maksym ; https://orcid.org/0000-0002-2399-5827 ddc:530 The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with time-dependent couplings is a challenging task and very little is known about the existence of solutions and their properties. In this work we develop a constructive approach for preparing matrix product states (MPS) via continuous unitary evolution. We provide an explicit construction of the operator that exactly implements the evolution of a given MPS along a specified direction in its tangent space. This operator can be written as a sum of local terms of finite range, yet it is in general non-Hermitian. Relying on the explicit construction of the non-Hermitian generator of the dynamics, we demonstrate the existence of a Hermitian sequence of operators that implements the desired MPS evolution with an error that decreases exponentially with the operator range. The construction is benchmarked on an explicit periodic trajectory in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary generating the dynamics over one period of the trajectory features an approximate MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results show that our construction is not only useful for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars—periodically driven models with quasilocal generators of dynamics that have exact MPS eigenstates in their spectrum. American Physical Society 2024 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/18488 https://research-explorer.ista.ac.at/download/18488/18489 Ljubotina M, Petrova E, Schuch N, Serbyn M. Tangent space generators of matrix product states and exact floquet quantum scars. <i>PRX Quantum</i>. 2024;5(4). doi:<a href="https://doi.org/10.1103/prxquantum.5.040311">10.1103/prxquantum.5.040311</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1103/prxquantum.5.040311 info:eu-repo/semantics/altIdentifier/e-issn/2691-3399 info:eu-repo/semantics/altIdentifier/wos/001346198800001 info:eu-repo/semantics/altIdentifier/arxiv/2403.12325 info:eu-repo/semantics/openAccess