# Regensburg 2019 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 16: Quantum Dynamics, Decoherence and Quantum Information

### DY 16.4: Vortrag

### Dienstag, 2. April 2019, 10:45–11:00, H6

**Dephasing and relaxation of topological states in extended quantum Ising models** — •Hannes Weisbrich, Wolfgang Belzig, and Gianluca Rastelli — Universität Konstanz

Inspired by recent progress in coupled arrays of qubits, we study the dephasing and relaxation dynamics of topological states in an extended class of quantum Ising chains of finite length [1]. We assume a local dephasing interaction of each spin with a local thermal bath, from which we derive a Lindblad equation. This kind of interaction preserves the parity in the system [2]. We demonstrate a correlation between the decoherence in the manyfold ground state subspace and the topology in the spin chain, characterized by a winding number g. In particular, in the topological regime and at low temperature, the decoherence rates can be exponentially suppressed. For the simple case of the transverse Ising model (g=1) this simply corresponds to the exponentially small overlap of the two localized Majorana zero energy modes of the equivalent Kitaev chain. We generalize this result in a chain with a three body, next nearest neighbor interaction (with g=2) in which the ground state subspace is fourfold degenerate with two ground states in each parity sector (even and odd), namely with four Majorana modes. For the second model, we analyze the decay rates and the probability of occupation of the different ground states as a function of the initial excited state.

[1] H. Weisbrich, W. Belzig, G. Rastelli (to be submitted);

[2] H. Weisbrich, C. Saussol, W. Belzig, G. Rastelli, Phys. Rev. A

98, 052109 (2018).