Topological Minimally Entangled States via Geometric Measure
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 …
Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
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…
Holographic encoding of universality in corner spectra
In numerical simulations of classical and quantum lattice systems, 2d corner transfer matrices (CTMs) and 3d corner tensors (CTs) are a useful tool to compute approximate contractions of infinite-size tensor networks. In this paper we show how the numerical CTMs and CTs can be used, {\it additionally\/}, to extract universal information from their spectra. We provide examples of this for classical and quantum systems, in 1d, 2d and 3d. Our results provide, in particular, practical evidence for a wide variety of models of the correspondence between $d$-dimensional quantum and $(d+1)$-dimensional classical spin systems. We show also how corner properties can be used to pinpoint quantum phase …