Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator

TL;DR

This paper demonstrates an exact Monte Carlo method to evaluate the strange correlator in AKLT states, enabling detection of symmetry-protected topological order across various lattice geometries and spin configurations.

Contribution

It introduces a direct wave function evaluation technique within the valence bond loop gas framework for AKLT states to compute the strange correlator exactly.

Findings

Exact evaluation of the strange correlator for multiple lattice geometries.

Introduction of the strange correlator loop winding number as a topological order indicator.

Validation of the method across different spin quantum numbers and lattice types.

Abstract

The strange correlator [Phys. Rev. Lett. 112, 247202 (2014)] has been proposed as a measure of symmetry protected topological order in one- and two-dimensional systems. It takes the form of a spin-spin correlation function, computed as a mixed overlap between the state of interest and a trivial local product state. We demonstrate that it can be computed exactly (asymptotically, in the Monte Carlo sense) for various Affleck-Kennedy-Lieb-Tasaki states by direct evaluation of the wave function within the valence bond loop gas framework. We present results for lattices with chain, square, honeycomb, cube, diamond, and hyperhoneycomb geometries. In each case, the spin quantum number S is varied such that 2S (the number of valence bonds emerging from each site) achieves various integer multiples of the lattice coordination number. We introduce the concept of strange correlator loop winding number and point to its utility in testing for the presence of symmetry protected topological order.