My main research interest is the non-equilibrium behavior of quantum many-body systems. In the past decades, condensed matter theory has mainly focused on understanding the equilibrium or linear response properties of condensed matter systems. Recent experimental advances in ultracold gases, nanostructures and pump-probe spectroscopy have opened up the exciting new field of non-equilibrium quantum many-body physics with many fundamental questions like thermalization in isolated systems, the role of integrability in non-equilibrium dynamics, physics beyond the linear response regime, etc. This has led to a lot of activity and my group is pursuing these questions using mainly analytical tools supplemented with numerical methods. We are also interested in developing new theoretical methods inspired by AdS/CFT correspondence, that is the duality between certain strong-coupling quantum field theories and geometrodynamcis like Einstein's theory of general relativity.

This is a link to an overview talk about non-equilibrium dynamics that I gave at the KITP.

Irreversible dynamics in quantum many-body systemsIrreversibility, despite being a necessary condition for thermalization, still lacks a sound understanding in the context of quantum many-body systems. In this work we approach this question by studying the behavior of generic many-body systems under imperfect effective time reversal, where the imperfection is introduced as a perturbation of the many-body state at the point of time reversal. Based on numerical simulations of the full quantum dynamics we demonstrate that observable echos occurring in this setting decay exponentially with a rate that is intrinsic to the system meaning that the dynamics is effectively irreversible.

[more...] Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light coneIn non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the time evolution of the correlation function of two local disjoint observables if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

[more...] Flow Equation HolographyThe Ryu-Takayanagi conjecture establishes a remarkable connection between quantum systems and geometry. Specifically, it relates the entanglement entropy to minimal surfaces within the setting of AdS/CFT correspondence. This Letter shows how this idea can be generalised to generic quantum many-body systems within a perturbative expansion where the region whose entanglement properties one is interested in is weakly coupled to the rest of the system. A simple expression is derived that relates a unitary disentangling flow in an emergent RG-like direction to the min-entropy of the region under consideration. Explicit calculations for critical free fermions in one and two dimensions illustrate this relation.

[more...] Photoexcitations in a 1D manganite model: From quasiclassical light absorption to quasiparticle relaxationsTh. Köhler, S. Rajpurohit, O. Schumann, F. R. A. Biebl, M. Sotoudeh, S. C. Kramer, P. E. Blöchl, S. Kehrein, S. R. Manmana,

arXiv:1610.07246We investigate the evolution of a photoexcitation in a correlated material over a wide range of time scales from femto- to nanoseconds. The system studied is a one-dimensional model of a manganite with correlated electron, spin, orbital, and lattice degrees of freedom. In a first step, the interaction of light with electrons considering the back-action is treated. Time-dependent matrix product states (MPS) methods are then used for the electronic quantum dynamics of the resulting photoexcitation. The emergence of quasiparticles from a fully correlated excitation is addressed. We study the relaxation of the non-equilibrium quasi-particle distribution with a linearized quantum-Boltzmann equation. Our investigation treats a model-Hamiltonian with parameters extracted from ab-initio calculations of Pr1?xCaxMnO3. This model is restricted to one dimension. The ground state phases for the entire composition range are determined and rationalized by a coarse grained polaron model. A pattern of antiferromagnetically coupled Zener polarons for the half-doped material is identified, which forms the basis for the dynamical calculations discussed above. We discuss the effect of the resulting magnetic microstructure on the relaxation times of the excitation.

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