Regensburg 2025 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 31: Topology: Quantum Hall Systems

TT 31.1: Invited Talk

Wednesday, March 19, 2025, 15:00–15:30, H31

Quantum Skyrmion Hall Effect — •Ashley Cook — MPI-PKS, Dresden, Germany

Motivated by recent discovery of additional topologically non-trivial phases of matter in lattice models beyond established classification schemes, we generalise the framework of the quantum Hall effect (QHE) to that of the quantum skyrmion Hall effect (QSkHE). This involves one key generalisation: considering particles on a two-sphere, which see a U(1) monopole, one can project to the lowest Landau level (LLL). Upon performing such a projection, the position coordinates become proportional to SU(2) generators by quenching of kinetic energy. An almost point-like LLL corresponds to matrix representation size for the SU(2) generators of N by N, with N small. The key generalisation is that such an almost point-like LLL with small orbital degeneracy can still host an intrinsically 2+1 dimensional topologically non-trivial many-body state. Equivalently, in regimes in which spin has previously been treated as a label (small N), spin encodes some finite number of spatial dimensions, in general. This many-body state can play the role, in the QSkHE, that a charged particle plays in the QHE.

Keywords: non-Fermi liquids; superconductivity; quantum gravity; quantum spin liquid; quantum Hall effect