@article{20646, abstract = {Describing general quantum many-body dynamics is a challenging task due to the exponential growth of the Hilbert space with system size. The time-dependent variational principle (TDVP) provides a powerful tool to tackle this task by projecting quantum evolution onto a classical dynamical system within a variational manifold. In classical systems, periodic orbits play a crucial role in understanding the structure of the phase space and the long-term behavior of the system. However, finding periodic orbits is generally difficult, and their existence and properties in generic TDVP dynamics over matrix product states have remained largely unexplored. In this work, we develop an algorithm to systematically identify and characterize periodic orbits in TDVP dynamics. Applying our method to the periodically kicked Ising model, we uncover both stable and unstable periodic orbits. We characterize the Kolmogorov-Arnold-Moser tori in the vicinity of stable periodic orbits and track the change of the periodic orbits as we modify the Hamiltonian parameters. We observe that periodic orbits exist at any value of the coupling constant of the kicked Ising model between prethermal and fully thermalizing regimes, but their relevance to quantum dynamics and imprint on quantum eigenstates diminishes as the system leaves the prethermal regime. Our results demonstrate that periodic orbits provide valuable insights into the TDVP approximation of quantum many-body evolution and establish a closer connection between quantum and classical chaos.}, author = {Petrova, Elena and Ljubotina, Marko and Yalniz, Gökhan and Serbyn, Maksym}, issn = {2691-3399}, journal = {PRX Quantum}, number = {4}, publisher = {American Physical Society}, title = {{Finding periodic orbits in projected quantum many-body dynamics}}, doi = {10.1103/tldp-kvkd}, volume = {6}, year = {2025}, } @article{18488, 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.}, author = {Ljubotina, Marko and Petrova, Elena and Schuch, Norbert and Serbyn, Maksym}, issn = {2691-3399}, journal = {PRX Quantum}, number = {4}, publisher = {American Physical Society}, title = {{Tangent space generators of matrix product states and exact floquet quantum scars}}, doi = {10.1103/prxquantum.5.040311}, volume = {5}, year = {2024}, } @article{15002, abstract = {The lattice Schwinger model, the discrete version of QED in 1 + 1 dimensions, is a well-studied test bench for lattice gauge theories. Here, we study the fractal properties of this model. We reveal the self-similarity of the ground state, which allows us to develop a recurrent procedure for finding the ground-state wave functions and predicting ground-state energies. We present the results of recurrently calculating ground-state wave functions using the fractal Ansatz and automized software package for fractal image processing. In certain parameter regimes, just a few terms are enough for our recurrent procedure to predict ground-state energies close to the exact ones for several hundreds of sites. Our findings pave the way to understanding the complexity of calculating many-body wave functions in terms of their fractal properties as well as finding new links between condensed matter and high-energy lattice models.}, author = {Petrova, Elena and Tiunov, Egor S. and Bañuls, Mari Carmen and Fedorov, Aleksey K.}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {5}, publisher = {American Physical Society}, title = {{Fractal states of the Schwinger model}}, doi = {10.1103/PhysRevLett.132.050401}, volume = {132}, year = {2024}, } @article{13138, abstract = {We consider the spin- 1 2 Heisenberg chain (XXX model) weakly perturbed away from integrability by an isotropic next-to-nearest neighbor exchange interaction. Recently, it was conjectured that this model possesses an infinite tower of quasiconserved integrals of motion (charges) [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)]. In this work we first test this conjecture by investigating how the norm of the adiabatic gauge potential (AGP) scales with the system size, which is known to be a remarkably accurate measure of chaos. We find that for the perturbed XXX chain the behavior of the AGP norm corresponds to neither an integrable nor a chaotic regime, which supports the conjectured quasi-integrability of the model. We then prove the conjecture and explicitly construct the infinite set of quasiconserved charges. Our proof relies on the fact that the XXX chain perturbed by next-to-nearest exchange interaction can be viewed as a truncation of an integrable long-range deformation of the Heisenberg spin chain.}, author = {Orlov, Pavel and Tiutiakina, Anastasiia and Sharipov, Rustem and Petrova, Elena and Gritsev, Vladimir and Kurlov, Denis V.}, issn = {2469-9969}, journal = {Physical Review B}, number = {18}, publisher = {American Physical Society}, title = {{Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain}}, doi = {10.1103/PhysRevB.107.184312}, volume = {107}, year = {2023}, }