Topological Minimally Entangled States via Geometric Measure

TL;DR

This paper demonstrates how to identify topological minimally entangled states in 2D systems using the geometric measure of entanglement, providing a new efficient method to extract topological information from ground states.

Contribution

It introduces a novel approach to find MES in topologically ordered systems via geometric entanglement minimization, applicable to various models and sizes.

Findings

Successfully identified MES in multiple topological models.

Showed geometric entanglement minimization reveals quasiparticle types.

Provided a scalable method for topological characterization from ground states.

Abstract

Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in [R. Orus, T.-C. Wei, O. Buerschaper, A. Garcia-Saez, arXiv:1406.0585] for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.