Advanced wave-function based methods for electron-phonon coupled systems

Fabian Heidrich-Meisner, Eric Jeckelmann


The main goal of this project is the development of efficient and versatile computational methods for studying correlated low-dimensional quantum systems with strongly fluctuating bosonic degrees of freedom. These methods are mainly based on one of the most powerful approaches for low-dimensional quantum many-body systems, the matrix-product-stateĀ  representation of quantum states. In the first funding period, we developed, implemented and tested numerical methods which allowed us to study the nonequilibrium dynamics of bosonic systems. In the second funding period we will improve the efficiency of these methods for systems in and out-of-equilibrium. In addition, we plan to adapt and test our algorithms in a broad variety of timely problems from condensed matter physics, mostly related to electron-phonon systems. These applications include phase transitions
and local entanglement entropy, nonequilibrium and dissipative transport through electron-phonon coupled nanostructures, time-resolved spectroscopy and photoinduced phase transitions in quasi-one-dimensional materials, as well as spin transport in spin-phonon coupled models.