Wednesday's seminar held at SISSA

[Cond.Matt. & Stat.Mech.Section]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR

 

Wednesday, 22 April   -   2:00 p.m.

 
 

SISSA, Santorio Building,  Room 005 (Ground floor)

 


Jacopo DE NARDIS    ( University of Amsterdam )

 

"Correlation functions of   in and out-of-equilibirum integrable models"


Abstract



Interacting integrable models, as the one-dimensional Lieb-Liniger point-interacting Bose gas and the XXZ spin chain, constitute a solid platform where to study highly excited states of interacting systems. In particular the structure of their excitations, together with the exact matrix elements, provides an efficient tool to evaluate dynamical correlation functions of equilibrium and non-equilibrium states. We will first show how an efficient numerical summation (ABACUS algorithm) over a restrict set of excitations around the steady state, provides the time evolution of the static density moment g2(x=0) after a quench from the free bosonic ground state (BEC state) to the Lieb-Liniger gas. In the limit of Tonks-Girardeau gas this summation can be exactly computed for two-body observables giving the post-quench time evolution of the momentum distribution function (De Nardis & Caux, J. Stat. Mech. (2014) P12012) . When the coupling constant is finite the analytical summation over the excitations is much harder to compute. We will however show how some recent results on the thermodynamics of the density form factors (De Nardis & Panfil, J. Stat. Mech. (2015) P02019) give hope in this direction. Finally we will comment on the recent surprising results on the role of the local conserved charges in determining the steady state after a quench in the XXZ spin chain (Wouters et al., Phys. Rev. Lett. 113, 117202 (2014)).