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Quantum many-body physics explores emergent properties of many interacting quantum particles, which often have no counterpart in classical systems. Of particular interest is the study of non-equilibrium dynamics of quantum many-body systems, which addresses fundamental questions at the intersection of condensed matter physics, statistical physics, atomic, molecular, and optical physics, and quantum information, and holds potential for advancing quantum technologies.

This Collection highlights theoretical and experimental original research and commissioned commentary on topics in quantum many-body dynamics. The original research part of the Collection is divided into three sections. The first section centers around non-equilibrium phenomena in interacting quantum systems, encompassing driven and dissipative dynamics, thermalization, dynamics of quantum information, as well as novel dynamical phases of matter such as many-body localization and time crystals. The second section is dedicated to methodological developments, including machine learning and quantum algorithms for describing quantum many-body systems. The final section showcases achievements in digital and analogue quantum simulations of many-body physics, with a focus on non-equilibrium states.

Can many-body systems be beneficial to designing quantum technologies? We address this question by examining quantum engines, where recent studies indicate potential benefits through the harnessing of many-body effects, such as divergences close to phase transitions. However, open questions remain regarding their real-world applications.

Digital quantum simulations of quantum many-body systems have emerged as one of the most promising applications of near-term quantum computing. This Perspective article provides an overview and an outlook on future developments in this field.

What is an optimal parameter landscape and geometric layout for a quantum processor so that its qubits are sufficiently protected for idling and simultaneously responsive enough for fast entangling gates? Quantum engineers pondering the dilemma might want to take a look on tools developed for many-body localization.

Understanding quantum topological states and the nature of their topological protection is an important fundamental question. By reinterpreting a past mode-switching experiment of an exciton-polariton condensate in a lattice, this work highlights the key role of collective many-body effects leading to the topological phase unwinding.

Studying out-of-equilibrium entanglement fluctuations is beyond the scope of current theories. Lim et al. present an analytical theory of fluctuations in long-time dynamics of entanglement in two classes of integrable lattice models, showing features reminiscent of universal mesoscopic fluctuations.

Periodically driven quantum systems have been extensively studied but with a predominant focus on long-time dynamics. Here, the authors study short-to-intermediate-time dynamics of an isolated many-body system, showing that its response to driving is supressed for the initial state close to thermal equilibrium.

Ultrafast spectroscopy enables characterization and control of non-equilibrium states. Here the authors introduce a stochastic thermodynamics approach to calculate entropy production in a material under ultrafast excitation, using ionic displacement data from time-resolved X-ray scattering experiments.

Many-body localization is observed in synthetic systems, but experiments on real materials with Coulomb interactions are vital for insights in higher dimensions. Stanley et al. report a prethermal regime in the dynamics of a 2D disordered electron system in Si MOSFETs and explore the effects of interaction range.

Many-body localized systems are believed to reach a stationary state without thermalizing. By using analytical and numerical calculations, the authors construct simple initial states for a typical MBL model, which neither equilibrate nor thermalize, similar to non-ergodic behavior in many-body scarred systems.

Artificial spin ice systems have been used to simulate a variety of phenomena including phase transitions. Here, the authors expand the scope of applications to encompass non-ergodic dynamics, by reporting real-space imaging of ergodicity transitions in a vortex-frustrated artificial spin ice.

Rydberg atom arrays are a promising platform for simulating many-body systems. The authors introduce a tensor-network method to compute phase diagrams of infinite arrays with long-range interactions and experimental-scale finite arrays, unveiling a new entangled phase and offering a guide for experiments.

Many-body localization is an important example of non-ergodic behaviour, however the conditions for its existence and stability are not fully established. Kloss et al establish theoretically and numerically the absence of many-body localization in a broad class of spin models respecting certain symmetries.

Some quantum spin models provide a condensed-matter realization of confinement, and previous work has shown that confinement affects the way they thermalize. Here the authors demonstrate for a many-body model with confinement that thermalization dynamics occurs in multiple stages, starting with a prethermal state.

Getting a grip on the chaotic properties of quantum systems is difficult. Now, the effect of translational invariance in space in time in an ensemble of random quantum circuits is shown to lead to largely universal scaling laws describing the system without the need of knowing microscopic details.

It has long been suggested that the inverse Fourier transform of neutron scattering data gives access to space- and time-resolved spin-spin correlations. Scheie et al. perform this procedure on high-precision experimental data from a 1D quantum antiferromagnet and uncover new features in short-term quench dynamics.

Recent work has reported a realization of a time crystal in the form of the Bose-Einstein condensate of magnons in superfluid ^{3}He. Here, the authors study the dynamics of a pair of such quantum time crystals and show that it closely resembles the evolution of a two-level system, modified by nonlinear feedback.

Superconducting quantum processors need to balance intentional disorder (to protect qubits) and nonlinear resonator coupling (to manipulate qubits), while avoiding chaotic instabilities. Berke et al. use the techniques of many-body localization theory to study the stability of current platforms against quantum chaos.

Discrete time crystals are described by a subharmonic response with respect to an external drive and have been mostly observed in closed periodically-driven systems. Here, the authors demonstrate a dissipative discrete time crystal in a Kerr-nonlinear optical microcavity pumped by two lasers.

The nonequilibrium regime provides an exciting frontier in the search for novel quantum phases of matter. Here, the authors show that optically driving a lightly-doped semiconductor can lead to the spontaneous formation of a dynamical quantum liquid crystalline phase with a rotating magnetization.

Understanding phase transitions in systems out of equilibrium is a topic of high interest. Here the author discusses the spontaneous antiunitary symmetry breaking leading to exceptional dynamical quantum phase transitions in driven many-body systems.

Discrete time crystals are typically characterized by a period doubled response with respect to an external drive. Here, the authors predict the emergence of rich dynamical phases with higher-order and fractional periods in clean spin-1/2 chains with long-range interactions.

A model of a classical discrete time crystal satisfying the criteria of persistent subharmonic response robust against thermal noise and defects has been lacking. Here, the authors show that these criteria are satisfied in one-dimensional probabilistic cellular automata with long-range interactions and bistability.

The relationship between thermalisation of classical system via dynamical chaos and the one of closed quantum systems is far from totally understood. Here, the authors shed light on this connection by projecting quantum dynamics to classical chaotic ones and determining its Lyapunov spectrum.

Typically, a quantum system that dissipates into the environment relaxes to a stationary state. Here the authors identify conditions under which dissipation prevents quantum many-body systems from reaching a steady state and they instead exhibit coherent oscillations.

Isolated many-body quantum systems do not thermalize with an external environment but in most cases the internal dynamics leads to the emergence of an effective thermal equilibrium for local degrees of freedom. Here the authors study this behaviour with a realization of a long-range spin model.

The entanglement in a quantum system between a small region and the surrounding environment contains details about the whole state. Nakagawa et al. find a formula for the entanglement entropy of a class of thermal-like states and show that it can be applied more broadly to identify equilibrating states.

Integrable models have an infinite number of conserved quantities but most realizations suffer from integrability breaking perturbations. Here the authors show that weakly driving such a system by periodic perturbations leads to large nonlinear responses governed by the approximate conservation laws.

The relaxation of closed macroscopic systems towards thermal equilibrium is an ubiquitous experimental fact, but very difficult to characterize theoretically. Here, the author establishes a quantitative description of such relaxation under arbitrary typical conditions, capturing well experimental data.

Boundary time crystals are gaining attention due to their distinctive features like persistent oscillations at the thermodynamic limit. This work shows that the boundary time crystal phase transition can be exploited for quantum-enhanced sensitivity, which bridges many-body physics and quantum metrology and hence triggers broad interest in the condensed matter and quantum technology communities.

Characterization of quantum chaotic systems involves a detailed understanding of their spectral properties. This work analyses such features in ultracold driven one-dimensional atomic gases, with emphasis on emerging universal scaling in early time deviations of the spectral form factor from random matrix theory predictions, outlining a potential experimental observational protocol.

Quantum many-body scarring, a peculiar phenomenon whereby a system thermalizes whilst it keeps returning to its initial state during the time evolution, has recently been observed in experiments on arrays of Rydberg atoms. The authors theoretically investigate the spectral properties of three Hamiltonians using a chain of bosons with density-dependent hopping, providing new insight in the phenomenon of many-body quantum scarring.

Variational autoregressive networks have been employed in the study of equilibrium statistical mechanics, chemical reaction networks and quantum many-body systems. Using these tools, Tang et al. develop a general approach to nonequilibrium statistical mechanics problems, such as dynamical phase transitions.

Variational approaches combined with machine learning are promising for solving quantum many-body problems, but they often suffer from scaling and optimization issues. Here the authors demonstrate that a stochastic representation of wavefunctions enables reducing the ground state search to standard regression.

Out-of-time-ordered correlators of local operators can quantify information scrambling in quantum many-body systems, but they are not easily accessible in experiments. Here the authors show that their global versions can be used for the same purpose and has been measured in nuclear magnetic resonance experiments.

Quantum Fisher information is a measure of entanglement that has been previously extracted from equilibrium spectra of quantum materials. Here the authors extend this approach to non-equilibrium systems probed by time-resolved resonant inelastic x-ray scattering measurements.

It was shown that the entanglement spectrum of topological systems is related to the energy spectrum of edge states, but only for gapped phases. Here the authors explain this relationship in terms of the wormhole effect in the path integral of the reduced density matrix and extend it beyond gapped phases.

A measure of symmetry breaking in a quantum many-body system could provide insight into its dynamics. Ares et al. introduce a subsystem measure of symmetry breaking dubbed entanglement asymmetry and apply it to quantum quench dynamics in spin chains, revealing a quantum analogue of the Mpemba effect.

Renormalisation group methods serve for finding analytic solutions, critical points and computing phase diagrams of many-body systems. Here the authors demonstrate that renormalisation group schemes can be constructed for undecidable many-body systems, giving rise to the types of renormalisation group flow which are strictly more unpredictable than chaotic flows.

Neural network representations of quantum states are hoped to provide an efficient basis for numerical methods without the need for case-by-case trial wave functions. Here the authors show that limited generalization capacity of such representations is responsible for convergence problems for frustrated systems.

The maximum precision achievable in quantum metrology is in general tractable only in few-body scenarios or in case of uncorrelated local noise. Here, the authors show a tensor networks method to compute such bounds in cases with large number of probes and short-range spatial and temporal noise correlations.

Developments of new computational methods for interacting electron systems have important implications for predictions of material properties. Chen and Haule combine variational techniques with diagrammatic quantum Monte Carlo to perform numerically exact calculations of electron gas properties, including the spin susceptibility and the dielectric function.

Simulating ultrafast quantum dissipation in molecular excited states is a strongly demanding computational task. Here, the authors combine tensor network simulation, entanglement renormalisation and machine learning to simulate linear vibronic models, and test the method by analysing singlet fission dynamics.

Significant improvements in numerical methods for quantum systems often come from finding new ways of representing quantum states that can be optimized and simulated more efficiently. Here the authors demonstrate a method to calculate exact neural network representations of many-body ground states.

Our understanding of open quantum many-body systems is limited because it is difficult to perform a theoretical treatment of both quantum and dissipative effects in large systems. Here the authors present a tensor network method that can find the steady state of 2D driven-dissipative many-body models.

One of the challenges in studies of quantum many-body physics is finding an efficient way to record the large system wavefunctions. Here the authors present an analysis of the capabilities of recently-proposed neural network representations for storing physically accessible quantum states.

Physicists’ understanding of interacting many-body systems often depends on finding an approximate description in terms of non-interacting particles. Here, the authors propose a systematic approach to identify the closest free particle description of a given model.

The hierarchical equations of motion approach is useful for the non-perturbative study of complex open quantum systems, which are simultaneously coupled to both bosonic and fermionic environments. To tackle these systems, the authors introduce an open-source software package (HierarchicalEOM.jl), characterized by a notable speed and accessibility to new users.

In quantum computing, simulating continuously evolving open quantum systems is key to describe dynamical processes on noisy quantum devices. Here, the authors present an open-source software package “Hamiltonian Open Quantum System Toolkit” (HOQST) for the simulation of open quantum system dynamics in Hamiltonian quantum computing based on the master equation approach.

Many problems in physics do not have an exact solution method, so their resolution has been sometimes possible only by guessing test functions. The authors apply Deep Reinforcement Learning (DRL) to control coherent transport of quantum states in arrays of quantum dots and demonstrate that DRL can solve the control problem in the absence of a known analytical solution even under disturbance conditions.

Metastable states found in superconductors and charge density wave materials are of fundamental interest. Vodeb et al. study the domain wall dynamics in 1T-TaS_{2} using scanning tunneling microscopy and a quantum annealer, finding that in both cases the dynamics is driven by spectrally similar noise.

Studying bounds on the speed of information propagation across interacting boson systems is notoriously difficult. Here, the authors find tight bounds for both the transport of boson particles and information propagation, for arbitrary time-dependent Bose-Hubbard-type Hamiltonians in arbitrary dimensions.

Thermal fluctuations can induce ordering in frustrated magnetic systems, yet the impact of quantum fluctuations is less explored. Here, in the controlled environment of a quantum annealer composed of superconducting qubits, the authors study a frustrated magnetic system finding that quantum fluctuations enhance magnetic correlations.

Atomically precise artificial lattices of dopant-based quantum dots offer a tunable platform for simulations of interacting fermionic models. By leveraging advances in fabrication and atomic-state control, Wang et al. report quantum simulations of the 2D Fermi-Hubbard model on a 3 × 3 few-dopant quantum dot array.

Strongly correlated condensed matter systems are among those for which quantum simulation should be able to give an advantage. Here, the authors use a translationally invariant tensor network technique to simulate a quantum critical system on a superconducting quantum processor.

Three-dimensional spin models with random hopping disorder are relevant to a large variety of physical systems. Here, the authors present an experimental realization of such a model in a Rydberg system with dipole-dipole coupling and show signatures of a localization-delocalization transition.

It was predicted that complex thermalizing behaviour can arise in many-body systems in the absence of disorder. Here, the authors observe non-ergodic dynamics in a tilted optical lattice that is distinct from previously studied regimes, and propose a microscopic mechanism that is due to emergent kinetic constrains.

The theoretical understanding of quantum many-body systems often involves properties of energy eigenstates but these are difficult to probe experimentally. Yang et al. propose an experiment that supports preparation and measurement of single eigenstates, enabling detailed studies of statistical physics.

Advances in the design and fabrication of superconducting devices enable physicists to design and monitor quantum electronic systems in synthetic environments. Here the authors observe how many-body effects influence the zero-point motion of a Josephson junction coupled to a high impedance transmission line.

The complete maximisation of the entanglement between two complementary blocks of spins due to the dynamics of spin chains remains to be observed. Here, Pitsios et al. simulate such dynamics by propagating single photons in an integrated photonic circuit.

Quantum simulation offers an unparalleled computational resource, but realizing it for fermionic systems is challenging due to their particle statistics. Here the authors report on the time evolutions of fermionic interactions implemented with digital techniques on a nine-qubit superconducting circuit.

In ultracold quantum gases, coherent nonequilibrium dynamics has been observed for bosons, but remained elusive in fermionic systems. Here, Will et al. demonstrate coherent quench dynamics in a hybrid quantum system composed of a metallic state of fermionic atoms and a Bose–Einstein condensate.

Geometrically frustrated spin systems are a class of statistical mechanical models that have received widespread attention, especially in condensed matter physics. This study experimentally demonstrates a quantum information processor that can simulate the behaviour of such frustrated spin system.

Studying long-range interactions in the controlled environment of trapped ultracold gases can help our understanding of fundamental many-body physics. Here the authors excite a gas of Rydberg atoms with a ps laser pulse, demonstrating behaviour consistent with many-body correlations beyond mean-field.

The goal of quantum simulation is to probe many-body phenomena in controlled systems, but Fermi-Hubbard phenomena are typically hard to simulate in cold atomic. Here, the authors simulate them with subsurface dopants in silicon, achieving a low effective temperature and reading out spin states with STM.

The robust implementation of gauge fields coupled to dynamical matter in large-scale quantum simulators is limited by the ever-present gauge-breaking errors. The authors propose an experimentally suitable scheme combining two-body interactions with weak fields, demonstrating its robustness against gauge breaking errors and its flexibility in the study of various models with Z2 gauge symmetry.

Pioneered in the cosmological setting, the Kibble–Zurek mechanism (KZM) describes the universal dynamics across a phase transition, leading to the breakdown of adiabatic dynamics and the formation of topological defects. The authors present an experimental study of the universal critical dynamics of a 1D quantum Ising chain driven across the paramagnet-to-ferromagnet phase transition using a trapped-ion quantum simulator, and characterize the probability distribution of topological defects, which is found in excellent agreement with theoretical predictions.