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Date | 14 October 2016 |
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Time | 14:00 -18:00 |

This event is part of a regular series of meetings on Quantum and Topological Matter, sponsored by Delta ITP. The objective is to bring together the theoretical physics communities in Amsterdam, Leiden and Utrecht. We encourage researchers from different areas in theoretical physics to participate!

*Title*

*Conformal QED in two-dimensional topological insulators*

*Chiral conformal field theory and the quantum Hall effect*

I will present a scheme for engineering a one-dimensional spinless p-wave superconductor hosting unpaired Majorana zero-energy modes, using an all electric setup with a spin-orbit coupled quantum wire in proximity to an s-wave superconductor. The required crossing of the Fermi level by a single spin-split energy band is ensured by employing a periodically modulated Rashba interaction, which, assisted by electron-electron interactions and a uniform Dresselhaus interaction, opens a gap at two of the spin-orbit shifted Fermi points. As the scheme calls for the assistance of e-e interactions, the microscopic Hamiltonian is cast in a low-energy effective bosonized description amenable to a renormalization group analysis. I will show the resulting phase diagram of the system and provide the minimum practical conditions for sustaining the topological phase in the laboratory.

*Conformal QED in two-dimensional topological insulators*

It has been shown recently that local four-fermion interactions on the edges of two-dimensional time-reversal-invariant topological insulators give rise to a new non-Fermi-liquid phase, called helical Luttinger liquid (HLL). In this talk, I provide a first-principle derivation of this non-Fermi-liquid phase based on the gauge-theory approach. Firstly, I derive a gauge theory for the edge states by simply assuming that the interactions between the Dirac fermions at the edge are mediated by a quantum dynamical electromagnetic field. Here, the massless Dirac fermions are confined to live on the one-dimensional boundary, while the (virtual) photons of the U(1) gauge field are free to propagate in all the three spatial dimensions that represent the physical space where the topological insulator is embedded. I then determine the effective 1+1-dimensional conformal field theory (CFT) given by the conformal quantum electrodynamics (CQED). By integrating out the gauge field in the corresponding partition function, I show that the CQED gives rise to a 1+1- dimensional Thirring model. The bosonized Thirring Hamiltonian describes exactly a HLL with a parameter K and a renormalized Fermi velocity that depend on the value of the fine-structure constant.

*Chiral conformal field theory and the quantum Hall effect*

The edge of a quantum Hall state can be described by a chiral conformal field theory (CFT). As this is an effective theory, one must also consider deformations to the chiral CFT. I will revisit the formulation of perturbation theory in the presence of such deformations by considering two examples that exhibit exact solution.

An ubiquitous feature of such an effective edge theory is that it exhibits emergent symmetries that were not parts of the underlying Hamiltonian. As a result, electron operators constructed out of the effective degrees of freedom form multiplets transforming under the emergent symmetry. Even though the deformations mentioned above can break the emergent symmetry, it is interesting to explicitly construct edge theories with exactly one electron operator. This is related to an open problem in classifying non-trivial CFT simple current with trivial tensor structure.

CWI Building, Euler Room, Science Park 123, Amsterdam.

More information on how to get there can be found here: http://www.cwi.nl/contact-and-route or GoogleMaps