Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization

TL;DR

This paper introduces an efficient tensor network method to detect topological phase transitions in 2d quantum systems using multipartite entanglement, providing sharper, faster results than traditional entanglement entropy approaches.

Contribution

The authors develop a tensor network algorithm based on Projected Entangled Pair States to compute topological geometric entanglement, enabling improved detection of topological transitions near criticality.

Findings

Accurately identifies topological phase transitions in 2d systems.

Method is significantly faster and more precise near critical points.

Extracts critical exponents and analyzes entanglement flow in topological phases.

Abstract

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on Projected Entangled Pair States to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation. When compared to tensor network methods for R\'enyi entropies, our approach produces almost perfect accuracies close to criticality and, on top, is orders of magnitude faster. The method can be adapted to deal with any topological state of the system, including minimally entangled ground states. It also allows to extract the critical exponent of the correlation length, and shows that there is no continuous entanglement-loss along renormalization group flows in topological phases.