Robin Steinigeweg

Pushing the Limits of the Eigenstate Thermalization Hypothesis towards Mesoscopic Quantum Systems

In the ongoing discussion on thermalization in closed quantum many-body systems, the eigenstate thermalization hypothesis has recently been proposed as a universal concept and has attracted considerable attention. So far this concept is, as the name states, hypothetical. The majority of attempts to overcome this hypothetical character are based on exact diagonalization, which implies for, e.g., spin systems a limitation of roughly 15 spins. In this Letter we present an approach that pushes this limit up to system sizes of roughly 35 spins, thereby going significantly beyond what is possible with exact diagonalization. A concrete application to a Heisenberg spin ladder which yields conclusive results is demonstrated.

Eigenstate thermalization within isolated spin-chain systems

The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic nonintegrable. While diagonal matrix elements for nonintegrable models comply with the eigenstate thermalization hypothesis, the integrable systems show evident deviations and similarity to properties of noninteracting many-fermion models. The finite-size scaling reveals that the crossover between the two regimes is given by a scale closely related to the scattering length. Low-frequency off-diagonal matrix elements related to dc transport quantities also follow in a generic system a behavior analogous to the eigenstate thermalization hypothesis, however, unrelated to one of the diagonal matrix elements.

Spin Transport in the XXZ Chain at Finite Temperature and Momentum

We investigate the role of momentum for the transport of magnetization in the spin-1/2 Heisenberg chain above the isotropic point at finite temperature and momentum. Using numerical and analytical approaches, we analyze the autocorrelations of density and current and observe a finite region of the Brillouin zone with diffusive dynamics below a cutoff momentum, and a diffusion constant independent of momentum and time, which scales inversely with anisotropy. Lowering the temperature over a wide range, starting from infinity, the diffusion constant is found to increase strongly while the cutoff momentum for diffusion decreases. Above the cutoff momentum diffusion breaks down completely.

Typicality approach to the optical conductivity in thermal and many-body localized phases

We study the frequency dependence of the optical conductivity

Relevance of the eigenstate thermalization hypothesis for thermal relaxation.

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Density dynamics in translationally invariant spin- 1 2 chains at high temperatures: A current-autocorrelation approach to finite time and length scales

of the Heisenberg spin-

Transition from diffusive to ballistic dynamics for a class of finite quantum models.

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Density dynamics from current auto-correlations at finite time- and length-scales

chain in the thermal and near the transition to the many-body localized phase induced by the strength of a random

Limited validity of the Kubo formula for thermal conduction in modular quantum systems

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Real-time broadening of nonequilibrium density profiles and the role of the specific initial-state realization

-directed magnetic field. Using the method of dynamical quantum typicality, we calculate the real-time dynamics of the spin-current autocorrelation function and obtain the Fourier transform