FQHE: Results on quasiparticle pinning and entanglement spectra using variational wavefunctions

QHE presents a rich set of experimentally observed quantum phenomena - from topological ordering and anyons to percolation like transitions and exciton condensates. Unlike other strongly interacting systems, much is known about the microscopic correlations in these systems thanks to first quantized real space variational composite fermion and parton wavefunctions for these states and their excitations. I will describe two sets of results based on variational descriptions of these systems. First pertains to disorder induced pinning of isolated quasiparticles of FQH states and its surprising similarity to the corresponding IQH problem [2,3]. Secondly I describe methods that allow computation of dominant eigenvalues of the reduced density matrices of extremely large composite fermion and parton states [1,4]. I use these to demonstrate the algebraic structures in the edge spectra of parton wavefunctions making use of the Li-Haldane conjecture. 

References
[1] A Anand, R A Patil, A C Balram, and G J Sreejith, PRB 106, 085136 (2022)
[2] Pu, G J Sreejith, J K Jain PRL 128, 116801
[3] P T Madathil, K A Villegas Rosales, C T Tai, Y J Chung, L N Pfeiffer, K W West, K W Baldwin, and M Shayegan, PRL. 130, 226503
[4] G J Henderson, G J Sreejith, S H Simon, in preparation