Trial wave functions for a composite Fermi liquid on a torus
Physical Review B American Physical Society 97:3 (2018) 035149
Abstract:
We study the two-dimensional electron gas in a magnetic field at filling fraction ν =1/2. At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.How SU(2)4 Anyons are Z3 Parafermions
SciPost Physics SciPost 3:6 (2017) 037
Abstract:
We consider the braid group representation which describes the non-abelian braiding statistics of the spin $1/2$ particle world lines of an SU(2)$_4$ Chern-Simons theory. Up to an abelian phase, this is the same as the non-Abelian statistics of the elementary quasiparticles of the $k=4$ Read-Rezayi quantum Hall state. We show that these braiding properties can be represented exactly using ${Z}_3$ parafermion operators.Breakdown of ergodicity in quantum systems: from solids to synthetic matter
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Royal Society 375:2108 (2017) 1-5
Quantum Hall physics: Hierarchies and conformal field theory techniques
REVIEWS OF MODERN PHYSICS 89:2 (2017) ARTN 025005
Quantum Hall Edges with Hard Confinement: Exact Solution beyond Luttinger Liquid
Physical Review B American Physical Society 95 (2017) 201108(R)