Spectral Gaps, Incompressibility and Fragmented Matrix-Product States in Fractional Quantum Hall Systems

Titel: Spectral Gaps, Incompressibility and Fragmented Matrix-Product States in Fractional Quantum Hall Systems

Abstract: 
The physics of fractional quantum Hall systems is characterised by the incompressibility of the fluid as well as the emergence of fractional charges at low temperatures.
These robust properties are faithfully described in terms of Haldane’s pseudo-potentials. 
I will start the talk by reviewing the mathematical set-up, basic properties and challenges related to these models.
A complete description of the ground state, excitations and a proof of the spectral gap, which is vital for a theoretical explanation of the spectral gap, is available in the thin-cylinder regime. 
In the second part of this talk I will sketch these results which rely on properties of the newly introduced class of fragmented matrix product states.