Andrey Gromov

Fractional quantum Hall effect is a strongly interacting topological phase of matter that has been experimentally observed and exists beyond the reasonable doubt. It naturally occurs in clean two-dimensional heterostructures at low temperatures and in strong magnetic fields. Groundstate physics of a fractional quantum Hall phase is traditionally described using topological quantum field theory, which encodes information about transport properties as well as statistics of topologically non-trivial quasiparticles aka anyons.

My research concerns two aspects of quantum Hall physics. First can be broadly characterized as geometric properties of quantum Hall states. Namely, how does a quantum Hall state respond to perturbations of sample geometry? This is mostly a thought experiment that can be utilized to extract observable properties of quantum Hall states, such as Hall viscosity and chiral central charge. Some publications on this topic are

Thermal Hall Effect and Geometry with Torsion

Boundary Effective Action for Quantum Hall States

Electromagnetic and gravitational responses of two-dimensional noninteracting electrons in a background magnetic field

Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect

Transport Signatures of the Hall Viscosity

Density-Curvature Response and Gravitational Anomaly

Second, concerns quantum Hall physics beyond the groundstate and beyond the topological field theory. Fractional quantum Hall phases support universally occurring collective modes. To describe the properties of these modes quantitatively, as well as to relate these modes to other observables, we developed the bimetric theory, which is a form of non-relativistic massive gravity. The relation to gravity appears because these collective modes have angular momentum 2 at small wave numbers. We put a lot of effort in proving through microscopic calculations as well as numerical simulations that bimetric theory is the right description of dynamics in the lowest Landau level. This body of work is unfinished because there is a lot of evidence for existence of higher energy mode with angular momentum >2. Pushing the effective theory to higher energies requires new ideas and is under investigation.

Bimetric Theory of Fractional Quantum Hall States

Quench Dynamics of Collective Modes in Fractional Quantum Hall Bilayers

Collective Excitations at Filling Factor $5/2$: The View from Superspace

Very high-energy collective states of partons in fractional quantum Hall liquids

Fractional quantum Hall systems near nematicity: Bimetric theory, composite fermions, and Dirac brackets

Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory

At certain filling fractions, such as 5/2, there is an emergent supersymmetry between the spin 2 and its "superpartner", the spin 3/2 mode.

Signatures of Supersymmetry in the $ν{=}5/2$ Fractional Quantum Hall Effect

Supergravity model of the Haldane-Rezayi fractional quantum Hall state