Mapping topological to conformal field theories through strange correlators

TL;DR

This paper extends the strange correlator concept to topological phases, linking lattice models to conformal field theories through ground state overlaps, revealing critical and symmetry-broken phases with topological defects.

Contribution

It introduces a novel approach to connect topological phases with conformal field theories using strange correlators and demonstrates this with lattice calculations for specific string-net models.

Findings

Critical and symmetry-broken phases identified via transfer matrices.

Conformal spectra obtained in different topological sectors.

Tensor network renormalization interpreted as strange correlator truncation.

Abstract

We extend the concept of strange correlators, defined for symmetry-protected phases in [You et al., Phys. Rev. Lett. 112, 247202 (2014)], to topological phases of matter by taking the inner product between string-net ground states and product states. The resulting two-dimensional partition functions are shown to be either critical or symmetry broken, as the corresponding transfer matrices inherit all matrix product operator symmetries of the string-net states. For the case of critical systems, those non-local matrix product operator symmetries are the lattice remnants of topological conformal defects in the field theory description. Following [Aasen et al., J. Phys. A 49, 354001 (2016)], we argue that the different conformal boundary conditions can be obtained by applying the strange correlator concept to the different topological sectors of the string-net obtained from Ocneanu's tube algebra. This is demonstrated by calculating the conformal field theory spectra on the lattice in the different topological sectors for the Fibonacci/hard-hexagon and Ising string-net. Additionally, we provide a complementary perspective on symmetry-preserving real-space renormalization by showing how known tensor network renormalization methods can be understood as the approximate truncation of an exactly coarse-grained strange correlator.