Tangent space generators of matrix product states and exact Floquet quantum scars
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912105069805568 |
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| author | Ljubotina, Marko Petrova, Elena Schuch, Norbert Serbyn, Maksym |
| author_facet | Ljubotina, Marko Petrova, Elena Schuch, Norbert Serbyn, Maksym |
| contents | 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 which 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 the error which 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 useful not only for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars -- periodically driven models with quasi-local generators of dynamics that have exact MPS eigenstates in their spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tangent space generators of matrix product states and exact Floquet quantum scars Ljubotina, Marko Petrova, Elena Schuch, Norbert Serbyn, Maksym Quantum Physics Statistical Mechanics Strongly Correlated Electrons 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 which 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 the error which 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 useful not only for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars -- periodically driven models with quasi-local generators of dynamics that have exact MPS eigenstates in their spectrum. |
| title | Tangent space generators of matrix product states and exact Floquet quantum scars |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2403.12325 |