K-matrices for quantum Hall states and beyond

Eddy Ardonne, Peter Bouwknegt, Kareljan Schoutens

Victor Gurarie, Chetan Nayak

Tankut Can, Michael Laskin, Paul B. Wiegmann

Eddy Ardonne, Peter Bouwknegt, Sathya Guruswamy +1 more

Two fundamental aspects of so-called non-Abelian quantum Hall states (the q-Pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-Abelian statistics of the quasihole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the K-matrices that describe the exclusion statistics of the fundamental excitations in these systems.

Paul Bracken

Liangdong Hu, Zhao Liu, W. Zhu

We investigate the response to modular transformations and the fractional statistics of Abelian multicomponent fractional quantum Hall (FQH) states. In particular, we analytically derive the modular matrices encoding the statistics of anyonic excitations for general Halperin states using the conformal field theories (CFTs). We validate our theory by several microscopic examples, including the spin-singlet state using the anyon condensation picture and the Halperin (221) state in a topological flat-band lattice model using numerical calculations. Our results, uncovering that the modular matrices and associated fractional statistics are solely determined by the $K$ matrix, further strengthens the correspondence between the two-dimensional (2D) CFTs and $(2+1)\mathrm{D}$ topological orders for multicomponent FQH states.