@article{21480, abstract = {We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as input classical shadows corresponding to local randomized measurements, and outputs the tensors of an MPO maximizing a suitably defined fidelity with the experimental state. The tensor optimization is carried out sequentially, similarly to the well-known density matrix renormalization group algorithm. Our approach is provably efficient under certain technical conditions expected to be met in short-range correlated states and in typical noisy experimental settings. Under the same conditions, we also provide an efficient scheme to estimate fidelities between the learned and the experimental states. We experimentally demonstrate our protocol by learning entangled quantum states of up to N = 96 qubits in a superconducting quantum processor. Our method upgrades classical shadows to large-scale quantum computation and simulation experiments.}, author = {Votto, Matteo and Ljubotina, Marko and Lancien, Cécilia and Cirac, J. Ignacio and Zoller, Peter and Serbyn, Maksym and Piroli, Lorenzo and Vermersch, Benoît}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {9}, publisher = {American Physical Society}, title = {{Learning mixed quantum states in large-scale experiments}}, doi = {10.1103/rbg2-f61m}, volume = {136}, year = {2026}, } @article{22408, abstract = {Solitons—localized wave packets that travel without spreading—play a central role in understanding transport and properties of nonlinear systems. In quantum many-body systems, however, such robust excitations are typically destroyed by thermalization. Here, we theoretically demonstrate the existence of solitonic excitations in high-energy states of Rydberg atom chains in the regime of strong nearest-neighbor Rydberg blockade. These localized wave packets propagate directionally atop a special class of reviving initial states related to quantum many-body scars and are capable of carrying energy. Exhibiting long coherence times, these states constitute a form of non-ergodic quantum dynamics and can be efficiently implemented on Rydberg atom simulators. In this work, in addition to a phenomenological description of solitons, we identify their counterpart in a classical nonlinear dynamical system, demonstrate their potential use in quantum information transfer, and conjecture their relevance for anomalous energy transport reported in numerical studies of Rydberg atom arrays.}, author = {Kerschbaumer, Aron and Desaules, Jean-Yves Marc and Ljubotina, Marko and Serbyn, Maksym}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Quasi-solitons in Rydberg atom chains}}, doi = {10.1038/s41467-026-75598-1}, volume = {17}, year = {2026}, } @article{21501, abstract = {Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy—known as zero modes—stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a U(1) particle-conservation symmetry. We use the U(1) East, which lacks inversion symmetry, and the inversion-symmetric U(1) East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a parametric increase in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single-particle physics and introduce the notion of collective bound states, a special kind of nonergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the U(1) North-East, and in the pairflip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models. }, author = {Nicolau Jimenez, Eulalia and Ljubotina, Marko and Serbyn, Maksym}, issn = {2691-3399}, journal = {PRX Quantum}, publisher = {American Physical Society}, title = {{Fragmentation, zero modes, and collective bound states in constrained models}}, doi = {10.1103/sl79-1xgb}, volume = {7}, year = {2026}, } @article{23027, abstract = {Kinetic constraints are generally expected to slow down dynamics in many-body systems, obstructing or even completely suppressing transport of conserved charges. Here, we show how gauge theories can defy this wisdom by yielding constrained models with faster-than-diffusive dynamics. We first show how, upon integrating out the gauge fields, one-dimensional U(1) lattice gauge theories are exactly mapped onto XX models with nonlocal constraints. This class of kinetically constrained models interpolates between free theories and highly constrained local fermionic models. We find that energy transport is superdiffusive over a broad parameter regime. Even more drastically, spin transport exhibits ballistic behavior, albeit with anomalous finite-volume properties as a consequence of gauge invariance. Our findings are relevant to current efforts in quantum simulations of gauge theory dynamics and anomalous hydrodynamics in closed quantum many-body systems.}, author = {Bhakuni, Devendra Singh and Verdel, Roberto and Desaules, Jean-Yves Marc and Serbyn, Maksym and Ljubotina, Marko and Dalmonte, Marcello}, issn = {2469-9969}, journal = {Physical Review B}, number = {14}, publisher = {American Physical Society}, title = {{Anomalously fast transport in nonintegrable lattice gauge theories}}, doi = {10.1103/3371-88bl}, volume = {114}, year = {2026}, } @article{23095, abstract = {The PXP chain was recently shown to exhibit superdiffusive energy transport with Kardar-Parisi-Zhang-like scaling, z ≈ 3/2, joining a growing number of spin chains with this exponent. An understanding of how this anomalous hydrodynamics emerges from microscopics is, however, still lacking. In this work, we show that finite-temperature energy transport in this model provides a window into the emergence of superdiffusion. At finite temperature, the energy autocorrelation function exhibits a crossover from short-time coherent dynamics to long-time hydrodynamics. The short-time behavior is dominated by a single magnon band and can be understood analytically. In momentum space, this regime is characterized by spectral weight near q = π. The damping time τ , which separates the short-time magnon-dominated behavior from the late-time hydrodynamics, grows rapidly upon cooling, consistent with an activated form τ (β) ∼ βeβ with a gap scale set by the magnon band. At longer times, the spectral weight transfers to q = 0 and the running decay exponent drifts toward the superdiffusive value z = 3/2. Finite-temperature energy transport therefore provides a bridge between microscopic magnon physics and late-time superdiffusion in the PXP model.}, author = {Shengtao, Jiang and Desaules, Jean-Yves Marc and Ljubotina, Marko and Scaffidi, Thomas}, issn = {2469-9969}, journal = {Physical Review B}, number = {8}, publisher = {American Physical Society}, title = {{Finite-temperature crossover from coherent magnons to energy superdiffusion in the PXP model}}, doi = {10.1103/mx9k-1mc6}, volume = {114}, year = {2026}, } @article{19664, abstract = {Persistent revivals recently observed in Rydberg atom simulators have challenged our understanding of thermalization and attracted much interest to the concept of quantum many-body scars (QMBSs). QMBSs are non-thermal highly excited eigenstates that coexist with typical eigenstates in the spectrum of many-body Hamiltonians, and have since been reported in multiple theoretical models, including the so-called PXP model, approximately realized by Rydberg simulators. At the same time, questions of how common QMBSs are and in what models they are physically realized remain open. In this Letter, we demonstrate that QMBSs exist in a broader family of models that includes and generalizes PXP to longer-range constraints and states with different periodicity. We show that in each model, multiple QMBS families can be found. Each of them relies on a different approximate algebra, leading to oscillatory dynamics in all cases. However, in contrast to the PXP model, their observation requires launching dynamics from weakly entangled initial states rather than from a product state. QMBSs reported here may be experimentally probed using Rydberg atom simulator in the regime of longer-range Rydberg blockades.}, author = {Kerschbaumer, Aron and Ljubotina, Marko and Serbyn, Maksym and Desaules, Jean-Yves Marc}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {16}, publisher = {American Physical Society}, title = {{Quantum many-body scars beyond the PXP model in Rydberg simulators}}, doi = {10.1103/PhysRevLett.134.160401}, volume = {134}, year = {2025}, } @article{19833, abstract = {Eigenstates of quantum many-body systems are often used to define phases of matter in and out of equilibrium; however, experimentally accessing highly excited eigenstates is a challenging task, calling for alternative strategies to dynamically probe nonequilibrium phases. In this work, we characterize the dynamical properties of a disordered spin chain, focusing on the spin-glass regime. Using tensor-network simulations, we observe oscillatory behavior of local expectation values and bipartite entanglement entropy. We explain these oscillations deep in the many-body localized spin-glass regime via a simple theoretical model. From perturbation theory, we predict the timescales up to which our analytical description is valid and confirm it with numerical simulations. Finally, we study the correlation length dynamics, which, after a long-time plateau, resume growing in line with renormalization group (RG) expectations. Our work suggests that RG predictions can be quantitatively tested against numerical simulations and experiments, potentially enabling microscopic descriptions of dynamical phases in large systems.}, author = {Brighi, Pietro and Ljubotina, Marko and Serbyn, Maksym}, issn = {2469-9969}, journal = {Physical Review B}, number = {22}, publisher = {American Physical Society}, title = {{Probing the many-body localized spin-glass phase through quench dynamics}}, doi = {10.1103/9fms-ygfz}, volume = {111}, year = {2025}, } @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{20709, abstract = {Non-Hermitian many-body localization (NH MBL) has emerged as a possible scenario for stable localization in open systems, as suggested by spectral indicators identifying a putative transition for finite system sizes. In this work, we shift the focus to dynamical probes, specifically the steady-state spin current, to investigate transport properties in a disordered, non-Hermitian XXZ spin chain. Through exact diagonalization for small systems and tensor-network methods for larger chains, we demonstrate that the steady-state current remains finite and decays exponentially with disorder strength, showing no evidence of a transition up to disorder values far beyond the previously claimed critical point. Our results reveal a stark discrepancy between spectral indicators, which suggest localization, and transport behavior, which indicates delocalization. This highlights the importance of dynamical observables in characterizing NH MBL and suggests that traditional spectral measures may not fully capture the physics of non-Hermitian systems. Additionally, we observe a noncommutativity of limits in system size and time, further complicating the interpretation of finite-size studies. These findings challenge the existence of NH MBL in the studied model and underscore the need for alternative approaches to understanding localization in non-Hermitian settings.}, author = {Brighi, Pietro and Ljubotina, Marko and Roccati, Federico and Balducci, Federico}, issn = {2643-1564}, journal = {Physical Review Research}, number = {4}, publisher = {American Physical Society}, title = {{Finite steady-state current defies non-Hermitian many-body localization}}, doi = {10.1103/crwj-x7j8}, volume = {7}, year = {2025}, } @article{18710, abstract = {We present an ab initio theoretical method to calculate the resonant Auger spectrum in the presence of ultrafast dissociation. The method is demonstrated by deriving the L-VV resonant Auger spectrum mediated by the 2p3/2−1σ* resonance in HCl, where the electronic Auger decay and nuclear dissociation occur on the same time scale. The Auger decay rates are calculated within the one-center approximation and are shown to vary significantly with the inter-nuclear distance. A quantum-mechanical description of dissociation is effectuated by propagating the corresponding Franck–Condon factors. The calculated profiles of Auger spectral lines resemble those of atomic Auger decay but here the characteristic tails extend towards lower electron kinetic energies, which reflect specific features of the potential energy curves. The presented method can describe the resonant Auger spectrum for an arbitrary speed of dissociation and simplifies to known approximations in the limiting cases.}, author = {Hrast, Mateja and Ljubotina, Marko and Zitnik, Matjaz}, issn = {1463-9076}, journal = {Physical Chemistry Chemical Physics}, number = {3}, pages = {1473--1482}, publisher = {Royal Society of Chemistry}, title = {{Ab initio Auger spectrum of the ultrafast dissociating 2p3/2−1σ* resonance in HCl}}, doi = {10.1039/d4cp03727h}, volume = {27}, 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{18176, abstract = {Introducing a class of SU(2) invariant quantum unitary circuits generating chiral transport, we examine the role of broken space-reflection and time-reversal symmetries on spin-transport properties. Upon adjusting parameters of local unitary gates, the dynamics can be either chaotic or integrable. The latter corresponds to a generalization of the space-time discretized (Trotterized) higher-spin quantum Heisenberg chain. We demonstrate that breaking of space-reflection symmetry results in a drift in the dynamical spin susceptibility. Remarkably, we find a universal drift velocity given by a simple formula, which, at zero average magnetization, depends only on the values of SU(2) Casimir invariants associated with local spins. In the integrable case, the drift velocity formula is confirmed analytically based on the exact solution of thermodynamic Bethe ansatz equations. Finally, by inspecting the large fluctuations of the time-integrated current between two halves of the system in stationary maximum-entropy states, we demonstrate violation of the Gallavotti-Cohen symmetry, implying that such states cannot be regarded as equilibrium ones. We show that the scaled cumulant generating function of the time-integrated current instead obeys a generalized fluctuation relation.}, author = {Zadnik, Lenart and Ljubotina, Marko and Krajnik, Žiga and Ilievski, Enej and Prosen, Tomaž}, issn = {2691-3399}, journal = {PRX Quantum}, number = {3}, publisher = {American Physical Society}, title = {{Quantum many-body spin ratchets}}, doi = {10.1103/PRXQuantum.5.030356}, volume = {5}, year = {2024}, } @article{18110, abstract = {We study a chaotic particle-conserving kinetically constrained model, with a single parameter which allows us to break reflection symmetry. Through extensive numerical simulations we find that the domain wall state shows a variety of dynamical behaviors from localization all the way to ballistic transport, depending on the value of the reflection breaking parameter. Surprisingly, such anomalous behavior is not mirrored in infinite-temperature dynamics, which appear to scale diffusively, in line with expectations for generic interacting models. However, studying the particle density gradient, we show that the lack of reflection symmetry affects infinite-temperature dynamics, resulting in an asymmetric dynamical structure factor. This is in disagreement with normal diffusion and suggests that the model may also exhibit anomalous dynamics at infinite temperature in the thermodynamic limit. Finally, we observe low-entangled eigenstates in the spectrum of the model, a telltale sign of quantum many-body scars.}, author = {Brighi, Pietro and Ljubotina, Marko}, issn = {2469-9969}, journal = {Physical Review B}, number = {10}, publisher = {American Physical Society}, title = {{Anomalous transport in the kinetically constrained quantum East-West model}}, doi = {10.1103/PhysRevB.110.L100304}, volume = {110}, year = {2024}, } @article{17493, abstract = {Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix, which allow us to reconstruct entropies and PT moments from information on local subsystems. This identification yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements providing a practical and common measurement scheme, we prove that our protocol requires only polynomially many measurements and postprocessing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators and provide numerical evidence that they are satisfied in more general, physically interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today’s quantum platforms.}, author = {Vermersch, Benoît and Ljubotina, Marko and Cirac, J. Ignacio and Zoller, Peter and Serbyn, Maksym and Piroli, Lorenzo}, issn = {2160-3308}, journal = {Physical Review X}, number = {3}, publisher = {American Physical Society}, title = {{Many-body entropies and entanglement from polynomially many local measurements}}, doi = {10.1103/physrevx.14.031035}, volume = {14}, year = {2024}, } @article{12839, abstract = {Universal nonequilibrium properties of isolated quantum systems are typically probed by studying transport of conserved quantities, such as charge or spin, while transport of energy has received considerably less attention. Here, we study infinite-temperature energy transport in the kinetically constrained PXP model describing Rydberg atom quantum simulators. Our state-of-the-art numerical simulations, including exact diagonalization and time-evolving block decimation methods, reveal the existence of two distinct transport regimes. At moderate times, the energy-energy correlation function displays periodic oscillations due to families of eigenstates forming different su(2) representations hidden within the spectrum. These families of eigenstates generalize the quantum many-body scarred states found in previous works and leave an imprint on the infinite-temperature energy transport. At later times, we observe a long-lived superdiffusive transport regime that we attribute to the proximity of a nearby integrable point. While generic strong deformations of the PXP model indeed restore diffusive transport, adding a strong chemical potential intriguingly gives rise to a well-converged superdiffusive exponent z≈3/2. Our results suggest constrained models to be potential hosts of novel transport regimes and call for developing an analytic understanding of their energy transport.}, author = {Ljubotina, Marko and Desaules, Jean Yves and Serbyn, Maksym and Papić, Zlatko}, issn = {2160-3308}, journal = {Physical Review X}, number = {1}, publisher = {American Physical Society}, title = {{Superdiffusive energy transport in kinetically constrained models}}, doi = {10.1103/PhysRevX.13.011033}, volume = {13}, year = {2023}, } @article{13963, abstract = {The many-body localization (MBL) proximity effect is an intriguing phenomenon where a thermal bath localizes due to the interaction with a disordered system. The interplay of thermal and nonergodic behavior in these systems gives rise to a rich phase diagram, whose exploration is an active field of research. In this paper, we study a bosonic Hubbard model featuring two particle species representing the bath and the disordered system. Using state-of-the-art numerical techniques, we investigate the dynamics of the model in different regimes, based on which we obtain a tentative phase diagram as a function of coupling strength and bath size. When the bath is composed of a single particle, we observe clear signatures of a transition from an MBL proximity effect to a delocalized phase. Increasing the bath size, however, its thermalizing effect becomes stronger and eventually the whole system delocalizes in the range of moderate interaction strengths studied. In this regime, we characterize particle transport, revealing diffusive behavior of the originally localized bosons.}, author = {Brighi, Pietro and Ljubotina, Marko and Abanin, Dmitry A. and Serbyn, Maksym}, issn = {2469-9969}, journal = {Physical Review B}, number = {5}, publisher = {American Physical Society}, title = {{Many-body localization proximity effect in a two-species bosonic Hubbard model}}, doi = {10.1103/physrevb.108.054201}, volume = {108}, year = {2023}, } @article{14334, abstract = {Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring conserved particle number and strong inversion-symmetry breaking due to facilitated hopping. We demonstrate that these models provide a generic example of so-called quantum Hilbert space fragmentation, that is manifested in disconnected sectors in the Hilbert space that are not apparent in the computational basis. Quantum Hilbert space fragmentation leads to an exponential in system size number of eigenstates with exactly zero entanglement entropy across several bipartite cuts. These eigenstates can be probed dynamically using quenches from simple initial product states. In addition, we study the particle spreading under unitary dynamics launched from the domain wall state, and find faster than diffusive dynamics at high particle densities, that crosses over into logarithmically slow relaxation at smaller densities. Using a classically simulable cellular automaton, we reproduce the logarithmic dynamics observed in the quantum case. Our work suggests that particle conserving constrained models with inversion symmetry breaking realize so far unexplored dynamical behavior and invite their further theoretical and experimental studies.}, author = {Brighi, Pietro and Ljubotina, Marko and Serbyn, Maksym}, issn = {2542-4653}, journal = {SciPost Physics}, keywords = {General Physics and Astronomy}, number = {3}, publisher = {SciPost Foundation}, title = {{Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models}}, doi = {10.21468/scipostphys.15.3.093}, volume = {15}, year = {2023}, } @article{12269, abstract = {We study the thermalization of a small XX chain coupled to long, gapped XXZ leads at either side by observing the relaxation dynamics of the whole system. Using extensive tensor network simulations, we show that such systems, although not integrable, appear to show either extremely slow thermalization or even lack thereof since the two cannot be distinguished within the accuracy of our numerics. We show that the persistent oscillations observed in the spin current in the middle of the XX chain are related to eigenstates of the entire system located within the gap of the boundary chains. We find from exact diagonalization that some of these states remain strictly localized within the XX chain and do not hybridize with the rest of the system. The frequencies of the persistent oscillations determined by numerical simulations of dynamics match the energy differences between these states exactly. This has important implications for open systems, where the strongly interacting leads are often assumed to thermalize the central system. Our results suggest that, if we employ gapped systems for the leads, this assumption does not hold.}, author = {Ljubotina, Marko and Roy, Dibyendu and Prosen, Tomaž}, issn = {2469-9969}, journal = {Physical Review B}, number = {5}, publisher = {American Physical Society}, title = {{Absence of thermalization of free systems coupled to gapped interacting reservoirs}}, doi = {10.1103/physrevb.106.054314}, volume = {106}, year = {2022}, } @article{12276, abstract = {Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of nontrivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states (MPSs). We compare counterdiabatic and leakage minimization approaches to the so-called local steering problem that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counterdiabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally, we apply our leakage minimization approach to construct quantum scars in the periodically driven nonintegrable Ising model.}, author = {Ljubotina, Marko and Roos, Barbara and Abanin, Dmitry A. and Serbyn, Maksym}, issn = {2691-3399}, journal = {PRX Quantum}, keywords = {General Medicine}, number = {3}, publisher = {American Physical Society}, title = {{Optimal steering of matrix product states and quantum many-body scars}}, doi = {10.1103/prxquantum.3.030343}, volume = {3}, year = {2022}, } @unpublished{12750, abstract = {Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring a conserved particle number and strong inversion-symmetry breaking due to facilitated hopping. We demonstrate that these models provide a generic example of so-called quantum Hilbert space fragmentation, that is manifested in disconnected sectors in the Hilbert space that are not apparent in the computational basis. Quantum Hilbert space fragmentation leads to an exponential in system size number of eigenstates with exactly zero entanglement entropy across several bipartite cuts. These eigenstates can be probed dynamically using quenches from simple initial product states. In addition, we study the particle spreading under unitary dynamics launched from the domain wall state, and find faster than diffusive dynamics at high particle densities, that crosses over into logarithmically slow relaxation at smaller densities. Using a classically simulable cellular automaton, we reproduce the logarithmic dynamics observed in the quantum case. Our work suggests that particle conserving constrained models with inversion symmetry breaking realize so far unexplored universality classes of dynamics and invite their further theoretical and experimental studies.}, author = {Brighi, Pietro and Ljubotina, Marko and Serbyn, Maksym}, booktitle = {arXiv}, title = {{Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models}}, doi = {10.48550/arXiv.2210.15607}, year = {2022}, }