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Nonequilibrium dynamics in the Hubbard model

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The (fermionic) Hubbard model is often considered as the paradigmatic minimal model for correlated electrons on lattices. Recent progress in the field of ultracold atom gases and pump-probe spectroscopy of correlated materials has stimulated interest in its nonequilibrium properties. Those can be probed by quantum quenches, i.e. nonadiabatic changes of parameters (e.g. the interaction) in real time. I will briefly review my earlier work based on perturbative and RG approaches to show that the response to small quenches within the Fermi liquid regime is generic, i.e. does not depend on the dimension (d>1) and lattice structure of the model [1]. Quenches across the phase transition are numerically challenging. A brief outlook to recent work [2] will be given which has shown that large similarities between the real time and the imaginary time evolution exist which may allow to probe dynamical critical exponents using imaginary time projector QMC methods with i-time dependent Hamiltonians.

[1] M. Moeckel and S. Kehrein, PRL 100 , 175702 (2008)

[2] C. De Grandi,1 A. Polkovnikov,2 and A. W. Sandvik arxiv 1301.2329 (2013)

This talk is part of the Electronic Structure Discussion Group series.

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