Gravitational anomaly spectroscopy of a Kitaev spin liquid
Abstract
The chiral central charge c measures the gravitational anomaly of a two-dimensional topological phase. It fixes the heat current carried along the edge. So far, 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 c is a spectroscopic quantity of the edge. A weak modulation of the edge couplings that travel along the edge is absorbed according to the Virasoro algebra. Normalized by the response to a static change of the same couplings, the absorbed weights obey Dn=2n⟨ L0⟩+c/12(n3−n), so that 𝒞≡2D2−4D1=c in any state of the ideal edge theory, thermal or not. The central charge thus appears in transition weights, although it cancels from excitation gaps. The ratio of line weights with and without a vison in the bulk, Λ=4hσ/c, needs no calibration and fixes the conformal spin hσ of the non-Abelian Ising anyon. For the Kitaev honeycomb spin liquid we find 𝒞=0.49999 and hσ=0.06250 on 7168 spins. Calibrating with the shift of the measured line itself gives c within about 1% on 96 spins and within 1% under 20% random coupling errors. Interacting edge Majoranas in a fixed flux sector, treated with DMRG, keep 𝒞 within 1.5% while the edge velocity changes by ±13%. An exact simulation of a quantum-processor protocol, including the native Floquet circuit, returns c within 3.5% on 96 to 600 spins.
Related
- Kitaev spin liquid in superconducting networks
- Mixed-State Topological Transition and Emergent Fractionalized Supersymmetry in the Non-Abelian Kitaev Spin Liquid
- Complete Entanglement Structure of the Kitaev Honeycomb Spin Liquid from Exact Tensor Networks
- Such stuff as magic is made on: compact operator algebra, stabilizer polytope and the structure of reduced density matrices in a Kitaev spin liquid
- Two superconducting pairing models with a Kitaev spin-liquid glue: microscopic kernel and parity alternation on odd-fold bond stars
BibTeX
@misc{ghosh2026gravitational,
title = {{Gravitational anomaly spectroscopy of a Kitaev spin liquid}},
author = {Kumar Ghosh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38704},
eprint = {2610.38704},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38704},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravitational anomaly spectroscopy of a Kitaev spin liquid
AU - Kumar Ghosh
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38704
UR - https://arxiv.org/abs/2610.38704
AB - The chiral central charge c measures the gravitational anomaly of a two-dimensional topological phase. It fixes the heat current carried along the edge. So far, 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 c is a spectroscopic quantity of the edge. A weak modulation of the edge couplings that travel along the edge is absorbed according to the Virasoro algebra. Normalized by the response to a static change of the same couplings, the absorbed weights obey D_n=2n⟨ L_0⟩+c/12(n^3−n), so that 𝒞≡2D_2−4D_1=c in any state of the ideal edge theory, thermal or not. The central charge thus appears in transition weights, although it cancels from excitation gaps. The ratio of line weights with and without a vison in the bulk, Λ=4h_σ/c, needs no calibration and fixes the conformal spin h_σ of the non-Abelian Ising anyon. For the Kitaev honeycomb spin liquid we find 𝒞=0.49999 and h_σ=0.06250 on 7168 spins. Calibrating with the shift of the measured line itself gives c within about 1% on 96 spins and within 1% under 20% random coupling errors. Interacting edge Majoranas in a fixed flux sector, treated with DMRG, keep 𝒞 within 1.5% while the edge velocity changes by ±13%. An exact simulation of a quantum-processor protocol, including the native Floquet circuit, returns c within 3.5% on 96 to 600 spins.
ER -