Two-dimensional quantum liquids from interacting non-Abelian anyons

Abstract

A set of localized, non-Abelian anyons - such as vortices in a p_x + i p_y superconductor or quasiholes in certain quantum Hall states - gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions between the anyons. Here we show that in two spatial dimensions this splitting selects a unique collective state as ground state of the interacting many-body system. This collective state can be a novel gapped quantum liquid nucleated inside the original parent liquid (of which the anyons are excitations). This physics is of relevance for any quantum Hall plateau realizing a non-Abelian quantum Hall state when moving off the center of the plateau.

5 pages, 6 figures

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Cited by in corpus (44)

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• A Short Introduction to Topological Quantum Computation
• Interacting Fibonacci anyons in a Rydberg gas
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Topological Phase Transitions in the Golden String-Net Model
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• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Disorder-induced Majorana metal in interacting non-Abelian anyon systems
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Low-energy sub-gap states in multi-channel Majorana wires
• Perturbed vortex lattices and the stability of nucleated topological phases
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Translation invariance, topology, and protection of criticality in chains of interacting anyons
• Majorana bands, Berry curvature, and thermal Hall conductivity in the vortex state of a chiral p-wave superconductor
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Quantum spin ladders of non-Abelian anyons
• Condensate-induced transitions and critical spin chains
• Integrable anyon chains: from fusion rules to face models to effective field theories
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Further insights into the thermodynamics of the Kitaev honeycomb model
• Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions
• One-dimensional itinerant interacting non-Abelian anyons
• Statistical dynamics of a non-Abelian anyonic quantum walk
• Phase diagram of superconductivity in the integer quantum Hall regime
• $Z_3$ generalization of the Kitaev's spin-1/2 model
• The $D(D_3)$-anyon chain: integrable boundary conditions and excitation spectra
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
• Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Effective models of doped quantum ladders of non-Abelian anyons
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• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Numerical simulation of non-abelian anyons
• Integrability in anyonic quantum spin chains via a composite height model
• Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands
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• From the Shastry-Sutherland model to the $J_1$-$J_2$ Heisenberg model
• 3D Non-Abelian Anyons: Degeneracy Splitting and Detection by Adiabatic Cooling
• Fibonacci topological phase in arrays of anyonic chains