Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks

Abstract

We propose a unified scheme to identify phase transitions out of the ${\mathbb{Z}}_2$ Abelian topological order, including the transition to a non-Abelian chiral spin liquid. Using loop gas and and string gas states [H.-Y. Lee, R. Kaneko, T. Okubo, N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)] on the star lattice Kitaev model as an example, we compute the overlap of minimally entangled states through transfer matrices. We demonstrate that, similar to the anyon condensation, continuous deformation of a ${\mathbb{Z}}_2$-injective projected entangled-pair state (PEPS) also allows us to study the transition between Abelian and non-Abelian topological orders. We show that the charge and flux anyons defined in the Abelian phase transmute into the $\sigma$ anyon in the non-Abelian topological order. Furthermore, we show that contrary to the claim in [Phys. Rev. B 101, 035140 (2020)], both the LG and SG states have infinite correlation length in the non-Abelian regime, consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian.

arXiv comment9 pages, 9 figures, published version

References in corpus (37)

• Anyons in an exactly solved model and beyond
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Coarse-graining renormalization by higher-order singular value decomposition
• An exact chiral spin liquid with non-Abelian anyons
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• PEPS as ground states: degeneracy and topology
• Anyons and matrix product operator algebras
• Topological order in PEPS: Transfer operator and boundary Hamiltonians
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Projected entangled-pair states can describe chiral topological states
• The Ground State Structure and Modular Transformations of Fractional Quantum Hall States on a Torus
• Shadows of Anyons
• Transfer Matrices and Excitations with Matrix Product States
• Chiral projected entangled-pair state with topological order
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Entanglement phases as holographic duals of anyon condensates
• Modular Matrices as Topological Order Parameter by Gauge Symmetry Preserved Tensor Renormalization Approach
• Tensor network wavefunction of $S=1$ Kitaev spin liquids
• Study of anyon condensation and topological phase transitions from a ${\mathbb{Z}}_4$ topological phase using Projected Entangled Pair States
• Condensation-Driven Phase Transitions in Perturbed String Nets
• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
• Tensor-network approach to phase transitions in string-net models
• The modular S-matrix as order parameter for topological phase transitions
• Tensor network approach to phase transitions of a non-Abelian topological phase
• Boson condensation and instability in the tensor network representation of string-net states
• Symmetry reduction induced by anyon condensation: a tensor network approach
• Determining non-Abelian topological order from infinite projected entangled pair states
• Determining topological order from infinite projected entangled pair states
• Abelian and non-Abelian chiral spin liquids in a compact tensor network representation

Cited by in corpus (3)

• Excitation spectrum of spin-1 Kitaev spin liquids
• Variational Tensor Network Operator
• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases