Determining non-Abelian topological order from infinite projected entangled pair states

Abstract

We generalize the method introduced in Phys. Rev. B 101, 041108 (2020) of extracting information about topological order from the ground state of a strongly correlated two-dimensional system represented by an infinite projected entangled pair state (iPEPS) to non-Abelian topological order. When wrapped on a torus the unique iPEPS becomes a superposition of degenerate and locally indistinguishable ground states. We find numerically symmetries of the iPEPS, represented by infinite matrix product operators (MPO), and their fusion rules. The rules tell us how to combine the symmetries into projectors onto states with well defined anyon flux. A linear structure of the MPO projectors allows for efficient determination for each state its second Renyi topological entanglement entropy on an infinitely long cylinder directly in the limit of infinite cylinder's width. The same projectors are used to compute topological $S$ and $T$ matrices encoding mutual- and self-statistics of emergent anyons. The algorithm is illustrated by examples of Fibonacci and Ising non-Abelian string net models.

arXiv commentnew appendices testing stability of the algorithm added

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Cited by in corpus (8)

• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Generating function for projected entangled-pair states
• Gauge symmetry of excited states in projected entangled-pair state simulations
• Variational Tensor Network Operator
• Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks
• Variational methods for characterizing matrix product operator symmetries
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers