Determining topological order from infinite projected entangled pair states

Abstract

We present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered systems, the iPEPS wrapped on a torus becomes a superposition of degenerate, locally indistinguishable ground states. Projectors in the form of infinite matrix product operators (iMPO) onto states with well-defined anyon flux are used to compute topological $S$ and $T$ matrices (encoding mutual- and self-statistics of emergent anyons). The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase. Our approach provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods. Moreover, we used numerically optimized iPEPS describing the ground state of the Kitaev honeycomb model in the toric code phase and obtained topological data in excellent agreement with theoretical prediction.

arXiv comment4+6 pages, 12 figures, published version

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Cited by in corpus (8)

• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• On the stability of topological order in tensor network states
• Determining non-Abelian topological order from infinite projected entangled pair states
• Stable and efficient differentiation of tensor network algorithms
• 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