arXiv subjects

Jonas Richter

Publications and source records attributed to Jonas Richter.

At least 19 recordsLinked to original sources

arXiv2024

Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions

We investigate the Lindblad equation in the context of boundary-driven magnetization transport in spin-$1/2$ chains. Our central question is whether the nonequilibrium steady state of the open system, including its buildup in time, can be described on the basis of the dynamics in the closed system. To this end, we rely on a previous work [Phys. Rev. B 108, L201119 (2023)], where a description in terms of spatio-temporal correlation functions has been suggested in the case of weak driving and small system-bath coupling. Because this work has focused on integrable systems and periodic boundary conditions, we here extend the analysis in three directions: We (i) consider nonintegrable systems, (ii) take into account open boundary conditions and other bath-coupling geometries, and (iii) provide a comparison to time-evolving block decimation. While we find that nonintegrability plays a minor role, the choice of the specific boundary conditions can be crucial, due to potentially nondecaying edge modes. Our large-scale numerical simulations suggest that a description based on closed-system correlation functions is an useful alternative to already existing state-of-the-art approaches.

cond-mat.stat-mech↗

arXiv2024

Temporal relaxation of disordered many-body quantum systems under driving and dissipation

Strong disorder inhibits thermalization in isolated quantum systems and may lead to many-body localization (MBL). In realistic situations, however, the observation of MBL is hindered by residual couplings of the system to an environment, which acts as a bath and pushes the system to thermal equilibrium. This paper is concerned with the transient dynamics prior to thermalization and studies how the relaxation of a disordered system is altered under the influence of external driving and dissipation. We consider a scenario where a disordered quantum spin chain is placed into a strong magnetic field that polarizes the system. By suddenly removing the external field, a nonequilibrium situation is induced and the decay of magnetization probes the degree of localization. We show that by driving the system with light, one can distinguish between different dynamical regimes as the spins are more or less susceptible to the drive depending on the strength of the disorder. We provide evidence that some of these signatures remain observable at intermediate time scales even when the spin chain is subject to noise due to coupling to an environment. From a numerical point of view, we demonstrate that the open-system dynamics starting from a class of experimentally relevant mixed initial states can be efficiently simulated by combining dynamical quantum typicality with stochastic unraveling of Lindblad master equations.

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arXiv2024

Simulating the dynamics of large many-body quantum systems with Schrödinger-Feynman techniques

The development of powerful numerical techniques has drastically improved our understanding of quantum matter out of equilibrium. Inspired by recent progress in the area of noisy intermediate-scale quantum devices, this paper highlights hybrid Schrödinger-Feynman techniques as an innovative approach to efficiently simulate certain aspects of many-body quantum dynamics on classical computers. To this end, we explore the nonequilibrium dynamics of two large subsystems, which interact sporadically in time, but otherwise evolve independently from each other. We consider subsystems with tunable disorder strength, relevant in the context of many-body localization, where one subsystem can act as a bath for the other. Importantly, studying the full interacting system, we observe that signatures of thermalization are enhanced compared to the reference case of having two independent subsystems. Notably, with the here proposed Schrödinger-Feynman method, we are able to simulate the pure-state survival probability in systems significantly larger than accessible by standard sparse-matrix techniques.

quant-ph↗

arXiv2024

Transport and integrability-breaking in non-Hermitian many-body quantum systems

Describing open quantum systems in terms of effective non-Hermitian Hamiltonians gives rise to non-unitary time evolution. In this paper, we study the impact of non-unitary dynamics on the emergent hydrodynamics in quantum systems with a global conservation law. To this end, we demonstrate how linear-response correlation functions can be generalized and interpreted in the case of non-Hermitian systems. Moreover, we show that dynamical quantum typicality provides an efficient numerical approach to evaluate such correlation functions, even though the non-unitary dynamics leads to subtleties that are absent in the Hermitian case. As a point of reference for our analysis, we consider the Hermitian spin-$1/2$ XXZ chain, whose high-temperature transport properties have been characterized extensively in recent years. Here, we explore the resulting hydrodynamics for different non-Hermitian perturbations of the XXZ chain. We also discuss the role of integrability by studying the complex energy-level statistics of the non-Hermitian quantum models.

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arXiv2023

Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions

State-of-the-art approaches to extract transport coefficients of many-body quantum systems broadly fall into two categories: (i) they target the linear-response regime in terms of equilibrium correlation functions of the closed system; or (ii) they consider an open-system situation typically modeled by a Lindblad equation, where a nonequilibrium steady state emerges from driving the system at its boundaries. While quantitative agreement between (i) and (ii) has been found for selected model and parameter choices, also disagreement has been pointed out in the literature. Studying magnetization transport in the spin-1/2 XXZ chain, we here demonstrate that at weak driving, the nonequilibrium steady state in an open system, including its buildup in time, can remarkably be constructed just on the basis of correlation functions in the closed system. We numerically illustrate this direct correspondence of closed-system and open-system dynamics, and show that it allows the treatment of comparatively large open systems, usually only accessible to matrix product state simulations. We also point out potential pitfalls when extracting transport coefficients from nonequilibrium steady states in finite systems.

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arXiv2023

Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems

We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few body operators in chaotic many-body systems, truncated below certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization. We discuss operator and system-size dependence of the energy scale of emergent unitary symmetry and put our findings in context of previous works exploring emergence of random-matrix behavior at small energy scales.

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arXiv2023

Real-time broadening of bath-induced density profiles from closed-system correlation functions

The Lindblad master equation is one of the main approaches to open quantum systems. While it has been widely applied in the context of condensed matter systems to study properties of steady states in the limit of long times, the actual route to such steady states has attracted less attention yet. Here, we investigate the nonequilibrium dynamics of spin chains with a local coupling to a single Lindblad bath and analyze the transport properties of the induced magnetization. Combining typicality and equilibration arguments with stochastic unraveling, we unveil for the case of weak driving that the dynamics in the open system can be constructed on the basis of correlation functions in the closed system, which establishes a connection between the Lindblad approach and linear response theory at finite times. In this way, we provide a particular example where closed and open approaches to quantum transport agree strictly. We demonstrate this fact numerically for the spin-1/2 XXZ chain at the isotropic point and in the easy-axis regime, where superdiffusive and diffusive scaling is observed, respectively.

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arXiv2023

Absence of localization in two-dimensional Clifford circuits

We analyze a Floquet circuit with random Clifford gates in one and two spatial dimensions. By using random graphs and methods from percolation theory, we prove in the two dimensional setting that some local operators grow at ballistic rate, which implies the absence of localization. In contrast, the one-dimensional model displays a strong form of localization characterized by the emergence of left and right-blocking walls in random locations. We provide additional insights by complementing our analytical results with numerical simulations of operator spreading and entanglement growth, which show the absence (presence) of localization in two-dimension (one-dimension). Furthermore, we unveil that the spectral form factor of the Floquet unitary in two-dimensional circuits behaves like that of quasi-free fermions with chaotic single particle dynamics, with an exponential ramp that persists till times scaling linearly with the size of the system. Our work sheds light on the nature of disordered, Floquet Clifford dynamics and its relationship to fully chaotic quantum dynamics.

quant-ph↗

arXiv2023

Hydrodynamics in long-range interacting systems with center-of-mass conservation

In systems with a conserved density, the additional conservation of the center of mass (dipole moment) has been shown to slow down the associated hydrodynamics. At the same time, long-range interactions generally lead to faster transport and information propagation. Here, we explore the competition of these two effects and develop a hydrodynamic theory for long-range center-of-mass-conserving systems. We demonstrate that these systems can exhibit a rich dynamical phase diagram containing subdiffusive, diffusive, and superdiffusive behaviors, with continuously varying dynamical exponents. We corroborate our theory by studying quantum lattice models whose emergent hydrodynamics exhibit these phenomena.

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arXiv2023

Transport and entanglement growth in long-range random Clifford circuits

Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher Rényi entropies. Here, we explore this phenomenon in a class of long-range random Clifford circuits with U$(1)$ symmetry where transport can be tuned from diffusive to superdiffusive. We unveil that the different hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to $S(t) \propto t^{1/z}$, where the dynamical transport exponent $z$ depends on the probability $\propto r^{-α}$ of gates spanning a distance $r$. For sufficiently small $α$, we show that the presence of hydrodynamic modes becomes irrelevant such that $S(t)$ behaves similarly in circuits with and without conservation law. We explain our findings in terms of the inhibited operator spreading in U$(1)$-symmetric Clifford circuits, where the emerging light cones can be understood in the context of classical Lévy flights. Our work sheds light on the connections between Clifford circuits and more generic many-body quantum dynamics.

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arXiv2022

Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems

We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum typicality, which exploits the fact that random pure quantum states can faithfully approximate ensemble averages, allowing the simulation of spin-$1/2$ systems with up to $40$ lattice sites. Due to the exponentially growing Hilbert space, we find that for such system sizes even a single random state is sufficient to yield results with extremely low noise that is negligible for most practical purposes. In contrast, a classical analog of typicality is missing. In particular, we demonstrate that, in order to obtain data with a similar level of noise in the classical case, extensive averaging over classical trajectories is required, no matter how large the system size. Focusing on (quasi-)one-dimensional spin chains and ladders, we find a remarkably good agreement between quantum and classical dynamics. This applies not only to cases where both the quantum and classical model are nonintegrable, but also to cases where the quantum spin-$1/2$ model is integrable and the corresponding classical $s\to\infty$ model is not. Our analysis is based on the comparison of space-time profiles of the spin and energy correlation functions, where the agreement is found to hold not only in the bulk but also in the tails of the resulting density distribution. The mean-squared displacement of the density profiles reflects the nature of emerging hydrodynamics and is found to exhibit similar scaling for quantum and classical models.

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arXiv2022

Many-body localization and delocalization dynamics in the thermodynamic limit

Disordered quantum systems undergoing a many-body localization (MBL) transition fail to reach thermal equilibrium under their own dynamics. Distinguishing between asymptotically localized or delocalized dynamics based on numerical results is however nontrivial due to finite-size effects. Numerical linked cluster expansions (NLCE) provide a means to tackle quantum systems directly in the thermodynamic limit, but are challenging for models without translational invariance. Here, we demonstrate that NLCE provide a powerful tool to explore MBL by simulating quench dynamics in disordered spin-$1/2$ two-leg ladders and Fermi-Hubbard chains. Combining NLCE with an efficient real-time evolution of pure states, we obtain converged results for the decay of the imbalance on long time scales and show that, especially for intermediate disorder below the putative MBL transition, NLCE outperform direct simulations of finite systems with open or periodic boundaries. Furthermore, while spin is delocalized even in strongly disordered Hubbard chains with frozen charge, we unveil that an additional tilted potential leads to a drastic slowdown of the spin imbalance and nonergodic behavior on accessible times. Our work sheds light on MBL in systems beyond the well-studied disordered Heisenberg chain and emphasizes the usefulness of NLCE for this purpose.

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arXiv2022

Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time

The Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal matrix elements are random numbers and the observables can be described by Random Matrix Theory (RMT). To what extent physical operators can be described by RMT, more precisely at which energy scale strict RMT description applies, is however not fully understood. We study this issue by introducing a novel numerical approach to probe correlations between matrix elements for Hilbert-space dimensions beyond those accessible for exact diagonalization. Our analysis is based on the evaluation of higher moments of operator submatrices, defined within energy windows of varying width. Considering nonintegrable quantum spin chains, we observe that genuine RMT behavior is absent even for narrow energy windows corresponding to time scales of the order of thermalization time $τ_\text{th}$ of the respective observables. We also demonstrate that residual correlations between matrix elements are reflected in the dynamics of out-of-time-ordered correlation functions.

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arXiv2022

Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians

Atypical eigenstates in the form of quantum scars and fragmentation of Hilbert space due to conservation laws provide obstructions to thermalization in the absence of disorder. In certain models with dipole and $U(1)$ conservation, the fragmentation results in subdiffusive transport. In this paper we study the interplay between scarring and weak fragmentation giving rise to anomalous hydrodynamics in a class of one-dimensional spin-$1$ frustration-free projector Hamiltonians, known as deformed Motzkin chain. The ground states and low-lying excitations of these chains exhibit large entanglement and critical slowdown. We show that at high energies the particular form of the projectors causes the emergence of disjoint Krylov subspaces for open boundary conditions, with an exact quantum scar being embedded in each subspace, leading to slow growth of entanglement and localized dynamics for specific out-of-equilibrium initial states. Furthermore, focusing on infinite temperature, we unveil that spin transport is subdiffusive, which we corroborate by simulations of constrained stochastic cellular automaton circuits. Compared to dipole moment conserving systems, the deformed Motzkin chain appears to belong to a different universality class with distinct dynamical transport exponent and only polynomially many Krylov subspaces.

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arXiv2021

Quantum simulation using noisy unitary circuits and measurements

Many-body quantum systems are notoriously hard to study theoretically due to the exponential growth of their Hilbert space. It is also challenging to probe the quantum correlations in many-body states in experiments due to their sensitivity to external noise. Using synthetic quantum matter to simulate quantum systems has opened new ways of probing quantum many-body systems with unprecedented control, and of engineering phases of matter which are otherwise hard to find in nature. Noisy quantum circuits have become an important cornerstone of our understanding of quantum many-body dynamics. In particular, random circuits act as minimally structured toy models for chaotic nonintegrable quantum systems, faithfully reproducing some of their universal properties. Crucially, in contrast to the full microscopic model, random circuits can be analytically tractable under a reasonable set of assumptions, thereby providing invaluable insights into questions which might be out of reach even for state-of-the-art numerical techniques. Here, we give an overview of two classes of dynamics studied using random-circuit models, with a particular focus on the dynamics of quantum entanglement. We will especially pay attention to potential near-term applications of random-circuit models on noisy-intermediate scale quantum (NISQ) devices. In this context, we cover hybrid circuits consisting of unitary gates interspersed with nonunitary projective measurements, hosting an entanglement phase transition from a volume-law to an area-law phase of the steady-state entanglement. Moreover, we consider random-circuit sampling experiments and discuss the usefulness of random quantum states for simulating quantum many-body dynamics on NISQ devices by leveraging the concept of quantum typicality. We highlight how emergent hydrodynamics can be studied by utilizing random quantum states generated by chaotic circuits.

quant-ph↗

arXiv2021

Nontrivial damping of quantum many-body dynamics

Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's golden rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping of a density matrix occurs in the interaction picture but not necessarily in the Schrödinger picture. We show that a nontrivial damping in the Schrödinger picture can emerge if the dynamics in the unperturbed system possesses rich features, for instance due to the presence of strong interactions. This suggestion has consequences for the time dependence of correlation functions. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system.

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arXiv2021

Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices

We present a comprehensive comparison of spin and energy dynamics in quantum and classical spin models on different geometries, ranging from one-dimensional chains, over quasi-one-dimensional ladders, to two-dimensional square lattices. Focusing on dynamics at formally infinite temperature, we particularly consider the autocorrelation functions of local densities, where the time evolution is governed either by the linear Schrödinger equation in the quantum case, or the nonlinear Hamiltonian equations of motion in the case of classical mechanics. While, in full generality, a quantitative agreement between quantum and classical dynamics can therefore not be expected, our large-scale numerical results for spin-$1/2$ systems with up to $N = 36$ lattice sites in fact defy this expectation. Specifically, we observe a remarkably good agreement for all geometries, which is best for the nonintegrable quantum models in quasi-one or two dimensions, but still satisfactory in the case of integrable chains, at least if transport properties are not dominated by the extensive number of conservation laws. Our findings indicate that classical or semi-classical simulations provide a meaningful strategy to analyze the dynamics of quantum many-body models, even in cases where the spin quantum number $S = 1/2$ is small and far away from the classical limit $S \to \infty$.

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arXiv2021

Quantum scars and bulk coherence in a symmetry-protected topological phase

Formation of quantum scars in many-body systems provides a novel mechanism for enhancing coherence of weakly entangled states. At the same time, coherence of edge modes in certain symmetry protected topological (SPT) phases can persist away from the ground state. In this work we show the existence of many-body scars and their implications on bulk coherence in such an SPT phase. To this end, we study the eigenstate properties and the dynamics of an interacting spin-$1/2$ chain with three-site "cluster" terms hosting a $\mathbb{Z}_2 \times \mathbb{Z}_2$ SPT phase. Focusing on the weakly interacting regime, we find that eigenstates with volume-law entanglement coexist with area-law entangled eigenstates throughout the spectrum. We show that a subset of the latter can be constructed by virtue of repeated cluster excitations on the even or odd sublattice of the chain, resulting in an equidistant "tower" of states, analogous to the phenomenology of quantum many-body scars. We further demonstrate that these scarred eigenstates support nonthermal expectation values of local cluster operators in the bulk and exhibit signatures of topological order even at finite energy densities. Studying the dynamics for out-of-equilibrium states drawn from the noninteracting "cluster basis", we unveil that nonthermalizing bulk dynamics can be observed on long time scales if clusters on odd and even sites are energetically detuned. In this case, cluster excitations remain essentially confined to one of the two sublattices such that inhomogeneous cluster configurations cannot equilibrate and thermalization of the full system is impeded. Our work sheds light on the role of quantum many-body scars in preserving SPT order at finite temperature and the possibility of coherent bulk dynamics in models with SPT order beyond the existence of long-lived edge modes.

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