Markus Heyl

Technische Universität Dresden, Dresden, Saxony, Germany

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Publications (25)71.76 Total impact

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    ABSTRACT: We study the dynamics and stability in a strongly-interacting resonantly-driven two-band model. Using exact numerical simulations, we find a stable regime at large driving frequencies where the dynamics is governed by a local Floquet Hamiltonian that is approximately conserved out to very long times. For slow driving, on the other hand, the system becomes unstable and heats up to infinite temperature. While thermalization is quick in these two regimes (but to different "temperatures"), in the crossover between them we find slow glassy dynamics: temporal fluctuations become strong and temporal correlations long-lived. Microscopically, we trace back the origin of this glassy dynamics to the appearance of rare Floquet many-body resonances, whose proliferation at lower driving frequency removes the metastable energy conservation, and thus produces thermalization to infinite temperature.
    No preview · Article · Dec 2015
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    ABSTRACT: Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterising quantum phases and quantum phase transitions. Developing protocols to detect and quantify entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, representing a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles via the dynamic susceptibility, i.e., with resources readily available in present cold atomic gas and condensed-matter experiments. This moreover establishes a fundamental connection between multipartite entanglement and many-body correlations contained in response functions, with profound implications close to quantum phase transitions. There, the quantum Fisher information becomes universal, allowing us to identify strongly entangled phase transitions with a divergent multipartiteness of entanglement. We illustrate our framework using paradigmatic quantum Ising models, and point out potential signatures in optical-lattice experiments.
    Full-text · Article · Sep 2015
  • Markus Heyl · Matthias Vojta
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    ABSTRACT: In this work we formulate the nonequilibrium dynamical renormalization group (ndRG). The ndRG represents a general renormalization-group scheme for the analytical description of the real-time dynamics of complex quantum many-body systems. In particular, the ndRG incorporates time as an additional scale which turns out to be important for the description of the long-time dynamics. It can be applied to both translational-invariant and disordered systems. As a concrete application, we study the real-time dynamics after a quench between two quantum critical points of different universality classes. We achieve this by switching on weak disorder in a one-dimensional transverse-field Ising model initially prepared at its clean quantum critical point. By comparing to numerically exact simulations for large systems, we show that the ndRG is capable of analytically capturing the full crossover from weak to infinite randomness. We analytically study signatures of localization in both real space and Fock space.
    No preview · Article · Sep 2015 · Physical Review B
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    ABSTRACT: When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. Exceptions to quantum thermalization have been predicted and observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize in spite of strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. Here we experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium. We observe the essential signatures of MBL: memory retention of the initial state, a Poissonian distribution of energy level spacings, and entanglement growth in the system at long times. Our platform can be scaled to higher numbers of spins, where detailed modeling of MBL becomes impossible due to the complexity of representing such entangled quantum states. Moreover, the high degree of control in our experiment may guide the use of MBL states as potential quantum memories in naturally disordered quantum systems.
    No preview · Article · Aug 2015
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    ABSTRACT: We investigate the resilience of symmetry-protected topological edge states at the boundaries of Kitaev chains in the presence of a bath which explicitly introduces symmetry-breaking terms. Specifically, we focus on single-particle losses and gains, violating the protecting parity symmetry, which could generically occur in realistic scenarios. In homogeneous systems, we show that the Majorana mode decays exponentially fast. However, we find that it is possible to substantially increase its life-time by eliminating the dissipative dynamics close to the edges. Most importantly, we demonstrate that the Majorana mode can be further stabilized by the inclusion of disorder where the decay of the Majorana converts into a stretched exponential form implying an exponential gain in stability compared to the homogeneous case. In particular, for pure loss dynamics we find a universal exponent $\alpha \simeq 2/3$. We show that this holds both in the Anderson and many-body localized regimes. Our results thus provide a concrete recipe to stabilize edge states even in the presence of symmetry-breaking environments.
    Preview · Article · Jul 2015 · Physical Review B
  • Markus Heyl
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    ABSTRACT: Dynamical quantum phase transitions (DQPTs) at critical times appear as non-analyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.
    No preview · Article · May 2015 · Physical Review Letters
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    ABSTRACT: Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals substantial correlations of the success probability with entanglement at the end of the protocol, but not with entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.
    Full-text · Article · Nov 2014 · Frontiers in Physics
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    ABSTRACT: In this Letter it is shown that dynamical quantum phase transitions in Loschmidt echos control the nonequilibrium dynamics of the order parameter after particular quantum quenches in systems with broken-symmetry phases. A direct connection between Loschmidt echos and the order parameter dynamics is established which links nonequilibrium microscopic probabilities to the system's macroscopic dynamical properties. These concepts are illustrated numerically using exact diagonalization for quantum quenches in the XXZ chain with initial Néel states. An outlook is given on how to explore these predictions experimentally with ultracold gases in optical lattices.
    No preview · Article · Nov 2014 · Physical Review Letters
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    Philipp Hauke · Markus Heyl
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    ABSTRACT: Ergodicity in quantum many-body systems is - despite its fundamental importance - still an open problem. Many-body localization provides a general framework for quantum ergodicity, and may therefore offer important insights. In this article, we study many-body localization and quantum ergodicity in long-range interacting Ising models with transverse-field disorder. We show analytically that this system enters a many-body localized phase at infinite temperature, irrespective of the disorder strength. We confirm our analytical predictions through extensive numerical simulations using exact diagonalization, and we find very good agreement to calculations based on the nonequilibrium dynamical renormalization group. To characterize and quantify quantum ergodicity, we introduce a measure for distances in Hilbert space. We show that in spin-1/2 systems it is equivalent to a simple local observable in real space, which can be measured in experiments of superconducting qubits, polar molecules, Rydberg atoms, and trapped ions.
    Full-text · Article · Oct 2014 · Physical Review B
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    Markus Heyl
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    ABSTRACT: In this work it is shown that the dynamics of the staggered magnetization in the XXZ chain after quantum quenches from initial Ne\'el states is controlled by dynamical quantum phase transitions in Loschmidt echos. A direct connection between Loschmidt echos and the order parameter dynamics is established which links nonequilibrium microscopic probabilities to the system's macroscopic dynamical properties. These concepts are illustrated numerically using exact diagonalization. An outlook is given how to generalize these findings to other observables and to other systems with symmetry-broken phases.
    Preview · Article · Mar 2014
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    Markus Heyl · Matthias Vojta
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    ABSTRACT: One necessary criterion for the thermalization of a nonequilibrium quantum many-particle system is ergodicity. It is, however, not sufficient in case where the asymptotic long-time state lies in a symmetry-broken phase but the initial state of nonequilibrium time evolution is fully symmetric with respect to this symmetry. In equilibrium one particular symmetry-broken state is chosen due to the presence of an infinitesimal symmetry-breaking perturbation. We study the analogous scenario from a dynamical point of view: Can an infinitesimal symmetry-breaking perturbation be sufficient for the system to establish a nonvanishing order during quantum real-time evolution? We study this question analytically for a minimal model system that can be associated with symmetry breaking, the ferromagnetic Kondo model. We show that after a quantum quench from a completely symmetric state the system is able to break its symmetry dynamically and discuss how these features can be observed experimentally.
    Preview · Article · Jan 2014 · Physical Review Letters
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    Markus Heyl · Matthias Vojta
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    ABSTRACT: We study the critical dynamics of a many-body quantum system after a quantum quench between two different quantum critical points of different universality classes. We achieve this by switching on weak disorder in a one-dimensional transverse-field Ising model initially prepared at its clean quantum critical point. We formulate a nonequilibrium dynamical renormalization group for the time evolution operator that is capable to capture analytically the full crossover from weak to infinite randomness. We analytically study signatures of localization both in real space and Fock space. We establish a general necessary criterion for ergodicity in Loschmidt echos.
    Preview · Article · Oct 2013
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    ABSTRACT: A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this paper we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely non-analytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.
    Full-text · Article · Mar 2013 · Physical Review Letters
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    M. Bukov · M. Heyl
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    ABSTRACT: We analyze the properties of a Luttinger liquid under the influence of a periodic driving of the interaction strength. Irrespective of the details the driven system develops an instability due to a parametric resonance. For slow and fast driving, however, we identify intermediate long-lived metastable states at constant time-averaged internal energies. Due to the instability perturbations in the fermionic density are amplified exponentially leading to the buildup of a superlattice. The momentum distribution develops a terrace structure due to scattering processes that can be associated with the absorption of quanta of the driving frequency.
    Preview · Article · Aug 2012 · Physical review. B, Condensed matter
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    M. Heyl · S. Kehrein
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    ABSTRACT: In this work we investigate the x-ray edge singularity problem realized in noninteracting quantum dots. We analytically calculate the exponent of the singularity in the absorption spectrum near the threshold and extend known analytical results to the whole parameter regime of local level detunings. Additionally, we highlight the connections to work distributions and to the Loschmidt echo.
    Preview · Article · Apr 2012 · Physical review. B, Condensed matter
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    ABSTRACT: We study quenches of the magnetic field in the transverse field Ising model. For quenches across the quantum critical point, the boundary partition function in the complex temperature-time-plane shows lines of Fisher zeroes that intersect the time axis, indicating non-analytic real time evolution in the thermodynamic limit (analogous to well-known thermodynamic phase transitions). We obtain exact analytical results for these dynamic transitions and show that the dynamic behavior cannot be obtained from a naive analytic continuation of the thermal equilibrium partition function: Real time evolution across this quantum critical point generates a new non-equilibrium energy scale. We argue that this behavior is expected to be generic for interaction quenches across quantum critical points in other models as well.
    No preview · Article · Feb 2012
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    ABSTRACT: We investigate the real-time dynamics of the energy density in spin-1/2 XXZ chains using two types of quenches resulting in initial states which feature an inhomogeneous distribution of local energies [1]. The first involves quenching bonds in the center of the chain from antiferromagnetic to ferromagnetic exchange interactions. The second quench involves an inhomogeneous magnetic field, inducing both, an inhomogeneous magnetization profile [2] and local energy density. The simulations are carried out using the adaptive time-dependent density matrix renormalization group algorithm. We analyze the time-dependence of the spatial variance of the bond energies and the local energy currents which both yield necessary criteria for ballistic or diffusive energy dynamics. For both setups, our results are consistent with ballistic behavior, both in the massless and the massive phase. For the massless regime, we compare our numerical results to bosonization and the non-interacting limit finding very good agreement. The velocity of the energy wave-packets can be understood as the average velocity of excitations induced by the quench. [4pt] [1] Langer et al. Phys. Rev. B in press; arXiv:1107.4136[0pt] [2] Langer et al. Phys. Rev. B 79, 214409 (2009)
    No preview · Article · Feb 2012
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    ABSTRACT: We study the real-time dynamics of the local energy density in the spin-1/2 XXZ chain starting from initial states with an inhomogeneous profile of bond energies. Numerical simulations of the dynamics of the initial states are carried out using the adaptive time-dependent density matrix renormalization group method. We analyze the time dependence of the spatial variance associated with the local energy density to classify the dynamics as either ballistic or diffusive. Our results are consistent with ballistic behavior both in the massless and the massive phase. We also study the same problem within Luttinger liquid theory and obtain that energy wave packets propagate with the sound velocity. We recover this behavior in our numerical simulations in the limit of very weakly perturbed initial states.
    Preview · Article · Nov 2011 · Physical review. B, Condensed matter
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    ABSTRACT: We investigate the real-time dynamics of the energy density in spin-1/2 chains and ladders, starting from initial states with an inhomogeneous profile of bond energies, extending our previous work on the dynamics of spin-density wave packets [1]. These simulations are carried out using the adaptive time-dependent density matrix renormalization group algorithm. We analyze the time-dependence of the spatial variance of the bond energies which yields necessary criteria for ballistic or diffusive energy dynamics. In the case of the XXZ chain, our results are consistent with ballistic behavior, both in the massless and the massive phase. For the massless regime, we compare our numerical results to predictions from bosonization for, e.g., the velocity that the initial perturbation spreads with. In the case of ladders, we find an involved dynamics whose qualitative interpretation is still under scrutiny. [4pt] [1] Langer et al. Phys. Rev. B 79, 214409 (2009)
    No preview · Article · Mar 2011
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    Markus Heyl · Stefan Kehrein
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    ABSTRACT: We show that in the quantum case any work distribution can be related to an equilibrium correlation function in an extended Hilbert space. As a consequence of this identification the Crooks relation is a restatement of the detailed balance principle for equilibrium correlation functions. The presented derivation serves as an alternative proof of the Crooks relation residing only on the detailed balance principle.
    Preview · Article · Dec 2010