6533b7d3fe1ef96bd126012c
RESEARCH PRODUCT
Topological Minimally Entangled States via Geometric Measure
Tzu-chieh WeiRoman OrusArtur Garcia-saezOliver Buerschapersubject
Statistics and ProbabilityPhysicsQuantum PhysicsFibonacci numberToric codeStrongly Correlated Electrons (cond-mat.str-el)High Energy Physics - Lattice (hep-lat)FOS: Physical sciencesStatistical and Nonlinear PhysicsTorusQuantum entanglementTopologyMultipartite entanglementCondensed Matter - Strongly Correlated ElectronsHigh Energy Physics - LatticeTopological orderStatistics Probability and UncertaintyAbelian groupQuantum Physics (quant-ph)Quantumdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-11-06 |