Tangent Space Generators of Matrix Product States and Exact Floquet Quantum Scars
Year: 2024
Type: article
Abstract: 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. Published by the American Physical Society 2024
Source: PRX Quantum
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,450
Awards: Non-Ergodic Quantum Matter: Universality, Dynamics and Control, G2595738051, G3398237449, G4157035715, G434337789, G4437173897, G4689434848, G5302217128, G5771549640, Symmetries and Entanglement in Quantum Matter, Kavli Institute for Theoretical Physics, G760448223, Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics, Entanglement Order Parameters, G9000274294
OpenAlex ID: W4403683638