title: Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization.
abstract: Topological order in two-dimensional (2D) quantum matter can be determined by the topological contribution to the entanglement Rényi 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 Rényi entropies, our approach produces almost perfect accuracies close to criticality and, additionally, 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 us 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.
authors.affiliation: Institute of Physics, Johannes Gutenberg University, 55099 Mainz, Germany.
authors.forename: Román
authors.initials: R
authors.lastname: Orús
authors.affiliation: C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, New York 11794-3840, USA.
authors.forename: Tzu-Chieh
authors.initials: TC
authors.lastname: Wei
authors.affiliation: Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada and Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: Oliver
authors.initials: O
authors.lastname: Buerschaper
authors.affiliation: C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, New York 11794-3840, USA.
authors.forename: Artur
authors.initials: A
authors.lastname: García-Saez