# Condensed-Matter Physics & Materials Science Seminar

## "GGE and applications for integrable models"

#### Presented by Garry Goldstein, Rutgers University

Thursday, June 4, 2015, 4:00 pm — ISB 2nd floor seminar room

We consider quenches of integrable models. We derive a Yudson representation applicable to finite sized systems. Using this representation we find expressions for the time dependence of density density and related correlation functions for an arbitrary quench of the repulsive LiebLiniger gas. We use this to show that the GGE formalism is applicable to the long time limit for quenches of the Lieb-Liniger gas with sufficiently regular initial states. We then show that no similar GGE formalism applies to quenches for integrable models with bound states (such as the XXZ model or the Hubbard model). We study several specific examples of quenches, in particular quenches where the initial state is a Mott insulator or has low entropy. We find the exact quasiparticle density for such quenches and use it to study the long time limit of some correlation functions for the system. We also consider quenches of confined systems, in particular the Lieb-linger gas in a box. We show that the GGE formalism applies to the long time average of such quenches. We use this observation to compute the long time average quasiparticle density for some quenches similar to the Quantum Newton's cradle quench experiment. We also compute various correlation functions for the system in particular the probability distribution for the particle velocity.

Hosted by: Robert Konik

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