The condensed matter theory group works on a wide range of modern topics centered around correlated electrons, quantum magnetism, nanostructures and non-equilibrium dynamics. We employ various numerical methods like QMC, DMRG and ED, and analytical approaches like field theoretic methods and flow equations.

# Research group Prof. Thomas Pruschke

# Research group Prof. Stefan Kehrein

The main focus of research in the group of Stefan Kehrein is the non-equilibrium dynamics of quantum many-body systems. Non-equilibrium quantum many-body systems have become a very active field of research since about 2005 due to both experimental progress in cold atomic gases and new theoretical methods for dealing with non-equilibrium time evolution.

Representation of excited states and topological order of the toric code in MERA |

The holographic contribution to the topological entanglement entropy on different scales. |

The holographic duality relates a field theory to a theory of (quantum) gravity in one dimension more. The extra dimension represents the scale of the RG transformation in the field theory. It has been conjectured that the tensor networks which arise during the real space renormalization procedure like the multi-scale entanglement renormalization ansatz (MERA) are a discretized version of the background of the gravity theory. We conside an explicit and tractable example, namely the dual network of the toric code, for which MERA can be performed analytically even for excited states. Furthermore, we show how to calculate topological entanglement entropy from the geometry of MERA.

[more...] Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model |

Distribution of zeros of the Loschmidt echo in the complex time plane for two different quenches. The zeros form areas in the complex plane . |

The notion of a dynamical quantum phase transition (DQPT) was recently introduced as the non-analytic behavior of the Loschmidt echo at critical times in the thermodynamic limit. In this work the quench dynamics in the ground state sector of the two-dimensional Kitaev honeycomb model are studied regarding the occurrence of DQPTs. For general two-dimensional systems of BCS-type it is demonstrated how the zeros of the Loschmidt echo coalesce to areas in the thermodynamic limit, implying that DQPTs occur as discontinuities in the second derivative. In the Kitaev honeycomb model DQPTs appear after quenches across a phase boundary or within the massless phase. In the 1d limit of the Kitaev honeycomb model it becomes clear that the discontinuity in the higher derivative is intimately related to the higher dimensionality of the non-degenerate model. Moreover, there is a strong connection between the stationary value of the rate function of the Loschmidt echo after long times and the occurrence of DQPTs in this model.

[more...]