Markus Heyl

Ludwig-Maximilian-University of Munich, München, Bavaria, Germany

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Publications (13)20.6 Total impact

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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 nonanalytic 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 Letter we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely nonanalytic 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.
    Physical Review Letters 03/2013; 110(13):135704. · 7.94 Impact Factor
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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.
    Physical review. B, Condensed matter 08/2012; 86(5).
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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.
    Physical review. B, Condensed matter 04/2012; 85(15).
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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.
    02/2012;
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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)
    02/2012;
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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)
    03/2011;
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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.
    Physical review. B, Condensed matter 01/2011; 84.
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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.
    12/2010;
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    M Heyl, S Kehrein
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    ABSTRACT: In this work we investigate the quench dynamics in the Kondo model on the Toulouse line in the presence of a local magnetic field. It is shown that this setup can be realized by either applying the local magnetic field directly or by preparing the system in a macroscopically spin-polarized initial state. In the latter case, the magnetic field results from a subtlety in applying the bosonization technique where terms that are usually referred to as finite-size corrections become important in the present non-equilibrium setting. The transient dynamics are studied by analyzing exact analytical results for the local spin dynamics. The timescale for the relaxation of the local dynamical quantities turns out to be exclusively determined by the Kondo scale. In the transient regime, one observes damped oscillations in the local correlation functions with a frequency set by the magnetic field.
    Journal of Physics Condensed Matter 09/2010; 22(34):345604. · 2.36 Impact Factor
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    P Wang, M Heyl, S Kehrein
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    ABSTRACT: We obtain exact results for the transport through a resonant level model (noninteracting Anderson impurity model) for rectangular voltage bias as a function of time. We study both the transient behavior after switching on the tunneling at time t = 0 and the ensuing steady state behavior. Explicit expressions are obtained for the ac current in the linear response regime and beyond for large voltage bias. Among other effects, we observe current ringing and PAT (photon-assisted tunneling) oscillations.
    Journal of Physics Condensed Matter 07/2010; 22(27):275604. · 2.36 Impact Factor
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    Markus Heyl, Stefan Kehrein
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    ABSTRACT: We show that work distributions and non-equilibrium work fluctuation theorems can be measured in optical spectra for a wide class of quantum systems. We consider systems where the absorption or emission of a photon corresponds to the sudden switch on or off of a local perturbation. For the particular case of a weak local perturbation, the Crooks relation establishes a universal relation in absorption as well as in emission spectra. Due to a direct relation between the spectra and work distribution functions this is equivalent to universal relations in work distributions for weak local quenches. As two concrete examples we treat the X-ray edge problem and the Kondo exciton.
    Physical Review Letters 06/2010; · 7.94 Impact Factor
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    ABSTRACT: We investigate systems of spinless one-dimensional chiral fermions realized, e.g., in the arms of electronic Mach-Zehnder interferometers, at high energies. Taking into account the curvature of the fermionic spectrum and a finite interaction range, we find a new scattering mechanism where high-energy electrons scatter off plasmons (density excitations). This leads to an exponential decay of the single-particle Green's function even at zero temperature with an energy-dependent rate. As a consequence of this electron-plasmon scattering channel, we observe the coherent excitation of a plasmon wave in the wake of a high-energy electron resulting in the buildup of a monochromatic sinusoidal density pattern. Comment: 5 pages, 3 figures; version as published
    Physical review. B, Condensed matter 02/2010;
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    M. Heyl, S. Kehrein
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    ABSTRACT: We investigate the Kondo model with time-dependent couplings that are periodically switched on and off. On the Toulouse line we derive exact analytical results for the spin dynamics in the steady state that builds up after an infinite number of switching periods. Remarkably, the universal long-time behavior of the spin-spin correlation function remains completely unaffected by the driving. In the limit of slow driving the dynamics becomes equivalent to that of a single interaction quench. In the limit of fast driving it is shown that the steady state cannot be described by some effective equilibrium Hamiltonian due to the observation that an incautious implementation of the Trotter formula is not correct. As a consequence, the steady state in the limit of fast switching serves as an example for the emergence of new quantum states not accessible in equilibrium.
    Physical review. B, Condensed matter 01/2010; 81(14).