Kolloquium der Theoretischen Physik
From Institute for Theoretical Physics II / University of Erlangen-Nuremberg
approximately every second Tuesday from 16:15 to 17:15 in Lecture Hall F
- 06.12.2016 Roman Orus (University of Mainz) Kitaev honeycomb tensor networks: exact unitary circuits and applications
The Kitaev honeycomb model is a paradigm of exactly-solvable models, showing non-trivial physical properties such as topological quantum order, abelian and non-abelian anyons, and chirality. Its solution is one of the most beautiful examples of the interplay of different mathematical techniques in condensed matter physics. In this talk I will show how to derive a tensor network (TN) description of the eigenstates of this spin-1/2 model in the thermodynamic limit, and in particular for its ground state. In our setting, eigenstates are naturally encoded by an exact 3d TN structure made of fermionic unitary operators, corresponding to the unitary quantum circuit building up the many-body quantum state. In the derivation I will review how the different "solution ingredients" of the Kitaev honeycomb model can be accounted for in the TN language, namely: Jordan-Wigner transformation, braidings of Majorana modes, fermionic Fourier transformation, and Bogoliubov transformation. The TN built in this way allows for a clear understanding of several properties of the model. In particular, I will show how the fidelity diagram is straightforward both at zero temperature and at finite temperature in the vortex-free sector, as well as properties of correlation functions. Finally, I will also discuss the pros and cons of contracting of our 3d TN down to a 2d Projected Entangled Pair State (PEPS) with finite bond dimension.
- 17.01.2017 Niels Lörch (University of Basel) Genuine quantum signatures in synchronization of anharmonic oscillators
Synchronization is an ubiquitious phenomenon in both nature and engineering, occuring for example in neuronal synchronization of the human brain or stabilization of power-grid networks. Whereas most research has focused on the classical domain, recent experimental progress allows to investigate how synchronization may differ in the quantum regime. We propose to use anharmonic oscillators to reveal genuine quantum signatures in synchronization, such as phase locking resonances originating from the discreteness of the energy spectrum, which are in stark contrast to any classical model. Experimental realizations are possible with trapped ions and superconducting circuits.