Steve Simon

Abstract:

Recent experiments [Banerjee et al, arXiv:1710.00492] have measured thermal conductance of the ν = 5/2 edge in a GaAs electron gas and found it to be quantized as K ≈ 5/2 (in appropriate dimensionless units). This result is unexpected, as prior numerical work predicts that the ν = 5/2 state should be the Anti-Pfaffian phase of matter, which should have quantized K = 3/2. The purpose of this paper is to propose a possible solution to this conflict: if the Majorana edge mode of the Anti-Pfaffian does not thermally equilibrate with the other edge modes, then K = 5/2 is expected. I briefly discuss a possible reason for this nonequilibration, and what should be examined further to determine if this is the case.

Abstract:

Many strongly correlated states, such as those arising in the fractional quantum Hall effect and spin liquids, are described by wavefunctions obtained by dividing particles into multiple clusters, constructing a readily evaluable wavefunction in each cluster, and (anti)symmetrizing across these clusters. We introduce a method to compute quantities such as energies and correlators, using Monte Carlo simulations for these states. Our framework overcomes the factorial scaling of explicit (anti)symmetrization, allowing for studies of systems beyond the reach of exact diagonalization.

Abstract:

We compute the degeneracy of energy levels in the Kitaev quantum double model for any discrete group $G$ on any planar graph forming the skeleton of a closed orientable surface of arbitrary genus. The derivation is based on the fusion rules of the properly identified vertex and plaquette excitations, which are selected among the anyons, i.e., the simple objects of the Drinfeld center $\mathcal{Z}(\mathrm{Vec}_G)$. These degeneracies are given in terms of the quantum dimensions of the anyons and allow one to obtain the exact finite-temperature partition function of the model, valid for any finite-size system.