Professor Fabian Essler

Abstract:

We consider the optical conductivity in the one dimensional Hubbard model in the metallic phase close to half filling. In this regime most of the spectral weight is located at frequencies above an energy scale Eopt that tends towards the optical gap in the Mott insulating phase for vanishing doping. Using the Bethe Ansatz we relate Eopt to thresholds of particular kinds of excitations in the Hubbard model. We then employ a mobile impurity models to analyze the optical conductivity for frequencies slightly above these thresholds. This entails generalizing mobile impurity models to excited states that are not highest weight with regards to the SU(2) symmetries of the Hubbard chain, and that occur at a maximum of the impurity dispersion.

Abstract:

In integrable many-particle systems, it is widely believed that the stationary state reached at late times after a quantum quench can be described by a generalized Gibbs ensemble (GGE) constructed from their extensive number of conserved charges. A crucial issue is then to identify a complete set of these charges, enabling the GGE to provide exact steady-state predictions. Here we solve this long-standing problem for the case of the spin- 1 / 2 Heisenberg chain by explicitly constructing a GGE which uniquely fixes the macrostate describing the stationary behavior after a general quantum quench. A crucial ingredient in our method, which readily generalizes to other integrable models, are recently discovered quasilocal charges. As a test, we reproduce the exact postquench steady state of the Néel quench problem obtained previously by means of the Quench Action method.