Spin quantum Hall transition on random networks: exact critical exponents via quantum gravity

TL;DR

This paper analytically determines the critical exponents of the spin quantum Hall transition on random networks by mapping it to classical percolation and applying quantum gravity techniques, confirming their relation to regular network exponents.

Contribution

It introduces an exact analytical method using quantum gravity to compute critical exponents for the spin quantum Hall transition on random networks, linking geometric randomness to known exponents.

Findings

Critical exponents are computed exactly for the transition.

The exponents relate to regular network exponents via the KPZ relation.

Results support the relevance of network geometry in quantum Hall transitions.

Abstract

We solve the problem of the spin quantum Hall transition on random networks using a mapping to classical percolation that focuses on the boundary of percolating clusters. Using tools of two-dimensional quantum gravity, we compute critical exponents that characterize this transition and confirm that these are related to the exponents for the regular (square) network through the KPZ relation. Our results demonstrate the relevance of the geometric randomness of the networks and support conclusions of numerical simulations of random networks for the integer quantum Hall transition.