8 April 2025 Tue 4 pm

The Girvin-Macdonald-Platzman (GMP) mode is a spin-2 gapped collective excitation characteristic of fractional quantum Hall states. It can be described as fluctuations of a unimodular metric associated with area-preserving diffeomorphisms, which are a fundamental feature of fractional quantum Hall fluids and explain their incompressibility. More recently, the GMP mode has been interpreted as fluctuations of a nematic order parameter related to the breaking of rotational symmetry. However, quantum area-preserving diffeomorphisms also suggest the existence of higher-spin collective modes that cannot be understood in terms of either a unimodular metric or a nematic order parameter. In this talk, I will discuss p-atic Hall phases, where the corresponding order parameters are given by higher-rank symmetric traceless tensors. In this framework, non-relativistic massive higher-spin fields naturally emerge, and their dynamics can be described using higher-spin Schrödinger-like actions. These effective actions can be derived from relativistic massive higher-spin theories in 2+1 dimensions by taking a suitable non-relativistic limit.

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