Tangent Space Generators of Matrix Product States and Exact Floquet Quantum Scars

Autor(en)

Marko Ljubotina, Elena Petrova, Norbert Schuch, Maksym Serbyn

Abstrakt

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.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation, Institut für Mathematik

Externe Organisation(en)

IST Austria - Institute of Science and Technology

Journal

PRX Quantum

Band

5

Seiten

040311-1 - 040311-18

Anzahl der Seiten

18

ISSN

2691-3399

DOI

https://doi.org/10.48550/arXiv.2403.12325

Publikationsdatum

10-2024

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik, 103024 Quantenfeldtheorie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/c38edece-7963-44ce-9c2a-25071e18ed99