Dynamical correlation functions of integrable quantum systems

• Applicant: Professor Dr. Michael Karbach
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 267822229

Experiments using cold atoms with and without optical lattices as well as experiments on trapped ions have recently given us access to the dynamics of quantum systems directly in the time domain. Dynamical correlation functions in such systems can by now be studied with single site addressability. This poses a serious challenge for theory to develop novel methods to calculate time-dependent correlations both in equilibrium and following a quantum quench.This project consists of two parts: (a) Dynamical correlations at finite temperatures in integrable one-dimensional quantum models will be calculated. We will combine a form factor approach, density-matrix renormalization group, and field theory calculations to obtain the full time dependence. The results will be benchmarks, helpful in explaining experimental data from neutron scattering and transport measurements, as well as providing input for planned experiments on cold atomic gases. (b) Quantum quenches and steady states after a quantum quench in integrable models will be investigated. The main focus is on understanding what the correct ensemble is to describe the steady state. This will require to construct all relevant conserved charges.

• DFG Programme: Research Units
• Subproject of: FOR 2316: Correlations in Integrable Quantum Many-Body Systems
• International Connection: Canada
• Co-Investigator: Professor Dr. Jesko Sirker