Frustrated topological symmetry breaking: geometrical frustration and anyon condensation

Abstract

We study the phase diagram of a topological string-net type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich phase diagram including both Abelian (${\mathbb{Z}}_2$) and non-Abelian ($\text{Ising}\times \overline{\text{Ising}}$) topologically ordered phases, as well as phases with broken translational symmetry. Interestingly, one of these phases simultaneously exhibits (Abelian) topological order and long-ranged order due to translational symmetry breaking, with non-trivial interactions between excitations in the topological order and defects in the long-ranged order. We introduce a variety of effective models, valid along certain lines in the phase diagram, which can be used to characterize both topological and symmetry-breaking order in these phases, and in many cases allow us to characterize the phase transitions that separate them. We use exact diagonalization and high-order series expansion to study areas of the phase diagram where these models break down, and to approximate the location of the phase boundaries.

16+11 pages

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Condensate induced transitions between topologically ordered phases
• Genons, twist defects, and projective non-Abelian braiding statistics
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Robustness of a perturbed topological phase
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• A quantum topological phase transition at the microscopic level
• Adiabatic Preparation of Topological Order
• Topological Phase Transitions in the Golden String-Net Model
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• Space-Time Geometry of Topological phases
• Wilson Line Picture of Levin-Wen Partition Functions
• Z2 topological liquid of hard-core bosons on a kagome lattice at 1/3 filling
• Phase diagram of an extended quantum dimer model on the hexagonal lattice
• Josephson Coupled Moore-Read States
• Russian doll spectrum in a non-Abelian string-net ladder

Cited by in corpus (19)

• Anyon condensation and its applications
• Symmetry enriched string-nets: Exactly solvable models for SET phases
• Generalized string-net models: A thorough exposition
• Bridging Perturbative Expansions with Tensor Networks
• Tensor-network approach to phase transitions in string-net models
• Vestigial anyon condensation in kagome quantum spin liquids
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• Composing topological domain walls and anyon mobility
• Antiferromagnetic magnons from fractionalized excitations
• Topological line in frustrated Toric code models
• Renormalization of Ising cage-net model and generalized foliation
• Bound states in string nets
• Quantum phase transitions in the $K$-layer Ising toric code
• Ising versus $SU(2{)}_2$ string-net ladder
• Quantum robustness of the toric code in a parallel field on the honeycomb and triangular lattice
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• Partially topological phase in a quantum loop gas model with tension and pressure
• Quantum phase transitions to topological Haldane phases in spin-one chains studied by linked-cluster expansions