Gravitational anomaly spectroscopy of a Kitaev spin liquid

Abstract

The chiral central charge $c$ measures the gravitational anomaly of a two-dimensional topological phase and fixes the heat current along its edge. It has been accessed through thermal transport, where phonons complicate the signal, or through wave-function probes that need a pure ground state. Here we show that a calibrated combination of directional edge absorption weights determines $c$. A modulation of the edge couplings that travels along the edge is absorbed according to the Virasoro algebra, and a static change of the same couplings measures the unknown probe normalization. Two harmonics then cancel the dependence on the edge state, so the estimator returns $c$ in any state of the ideal edge theory. A ratio of line weights with and without a vison gives the conformal spin of the Ising anyon. For the Kitaev honeycomb model, exact calculations recover $c=1/2$ and $h_{\sigma }=1/16$ to $10^{-5}$ and give $c$ within about $1\%$ on 96 spins. Compiled into gate circuits on the physical spins of a square-lattice quantum simulator, the protocol returns $c$ within $5\%$ on 48 qubits. For stochastic gate errors it requires two-qubit error rates of $10^{-6}$ to $10^{-5}$.

arXiv comment15 pages 6 figures