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.

4+6 pages, 12 figures, published version

References in corpus (20)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Identifying Topological Order by Entanglement Entropy
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Characterizing topological order by studying the ground states of an infinite cylinder
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Explicit tensor network representation for the ground states of string-net models
• Gauging quantum states: from global to local symmetries in many-body systems
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Infinite size density matrix renormalization group, revisited
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• General procedure for determining braiding and statistics of anyons using entanglement interferometry
• Quantum phases of the frustrated XY models on the honeycomb lattice
• Constructing topological models by symmetrization: A PEPS study
• Nature of continuous phase transitions in interacting topological insulators
• Numerical Observation of Parafermion Zero Modes and their Stability in 2D Topological States

Cited by in corpus (1)

• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states