Per Moosavi: Non-local Luttinger model out of equilibrium: Exact results and emergence of generalized hydrodynamics

The Luttinger model with finite-range interactions is an exactly solvable model in 1+1 dimensions somewhere between conformal and Bethe-ansatz integrable ones. I will show how exact analytical results can be computed for the time evolution of this non-local Luttinger model following an inhomogeneous quench from initial states defined by smooth temperature and chemical-potential profiles. These results demonstrate that the finite-range interactions give rise to dispersive effects that are not present in the conformal case of point-like interactions. Combing the same methods with the recent proposal of generalized hydrodynamics, one finds that this model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. These results are shown to emerge from the exact analytical ones at the relevant time and length scales. As such, the non-local Luttinger model provides a simple tractable example to analytically study the emergence of hydrodynamics in a quantum many-body system.