Study of anyon condensation and topological phase transitions from a ${\mathbb{Z}}_4$ topological phase using Projected Entangled Pair States

Abstract

We use Projected Entangled Pair States (PEPS) to study topological quantum phase transitions. The local description of topological order in the PEPS formalism allows us to set up order parameters which measure condensation and deconfinement of anyons, and serve as a substitute for conventional order parameters. We apply these order parameters, together with anyon-anyon correlation functions and some further probes, to characterize topological phases and phase transitions within a family of models based on a ${\mathbb{Z}}_4$ symmetry, which contains ${\mathbb{Z}}_4$ quantum double, toric code, double semion, and trivial phases. We find a diverse phase diagram which exhibits a variety of different phase transitions of both first and second order which we comprehensively characterize, including direct transitions between the toric code and the double semion phase.

21+6 pages

References in corpus (13)

• Criticality, the area law, and the computational power of PEPS
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Condensate induced transitions between topologically ordered phases
• Valence Bond Solids for Quantum Computation
• Ground state fidelity from tensor network representations
• Resonating valence bond states in the PEPS formalism
• Explicit tensor network representation for the ground states of string-net models
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• Transfer Matrices and Excitations with Matrix Product States
• Entanglement phases as holographic duals of anyon condensates
• Semionic resonating valence bond states
• Tensor-product representations for string-net condensed states

Cited by in corpus (31)

• Simulating excitation spectra with projected entangled-pair states
• Anyon condensation and the color code
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• Pauli stabilizer models of twisted quantum doubles
• Classification of phases for mixed states via fast dissipative evolution
• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• From trivial to topological paramagnets: The case of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries in two dimensions
• Entanglement order parameters and critical behavior for topological phase transitions and beyond
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• Tensor network state approach to quantum topological phase transitions and their criticalities of ${\mathbb{Z}}_2$ topologically ordered states
• Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries
• A gapped SU(3) spin liquid with Z_3 topological order
• On tensor network representations of the (3+1)d toric code
• Determining non-Abelian topological order from infinite projected entangled pair states
• Gapped $Z_2$ spin liquid in the breathing kagome Heisenberg antiferromagnet
• Determining topological order from infinite projected entangled pair states
• Quantum trimer models and topological SU(3) spin liquids on the kagome lattice
• Topological Spin Liquids: Robustness under perturbations
• Anomalous domain wall condensation in a modified Ising chain
• String order parameters for symmetry fractionalization in an enriched toric code
• Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks
• Continuous topological phase transition between ${\mathbb{Z}}_2$ topologically ordered phases
• Topological Phase Transitions Induced by Varying Topology and Boundaries in the Toric Code
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
• Variational methods for characterizing matrix product operator symmetries
• Condensation of non-Abelian $SU(3{)}_{N_f}$ anyons in a one-dimensional fermion model
• Skeleton of isometric Tensor Network States for Abelian String-Net Models