Quantum spin ladders of non-Abelian anyons

Abstract

Quantum ladder models, consisting of coupled chains, form intriguing systems bridging one and two dimensions and have been well studied in the context of quantum magnets and fermionic systems. Here we consider ladder systems made of more exotic quantum mechanical degrees of freedom, so-called non-Abelian anyons, which can be thought of as certain quantum deformations of ordinary SU(2) spins. Such non-Abelian anyons occur as quasiparticle excitations in topological quantum fluids, including p_x + i p_y superconductors, certain fractional quantum Hall states, and rotating Bose-Einstein condensates. Here we use a combination of exact diagonalization and conformal field theory to determine the phase diagrams of ladders with up to four chains. We discuss how phenomena familiar from ordinary SU(2) spin ladders are generalized in their anyonic counterparts, such as gapless and gapped phases, odd/even effects with the ladder width, and elementary `magnon' excitations. Other features are entirely due to the topological nature of the anyonic degrees of freedom.

12 pages, 17 figures, 3 tables, 2 references added

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Interacting anyons in topological quantum liquids: The golden chain
• A short introduction to Fibonacci anyon models
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Collective states of interacting Fibonacci anyons
• Microscopic models of interacting Yang-Lee anyons
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Experimental signatures of non-Abelian statistics in clustered quantum Hall states

Cited by in corpus (22)

• Topological Phase Transitions in the Golden String-Net Model
• Criticality in Translation-Invariant Parafermion Chains
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Translation invariance, topology, and protection of criticality in chains of interacting anyons
• Matrix product states for anyonic systems and efficient simulation of dynamics
• Braiding of non-Abelian anyons using pairwise interactions
• Prime Suspects in a Quantum Ladder
• Quantum phases of a chain of strongly interacting anyons
• One-dimensional itinerant interacting non-Abelian anyons
• Finite Density Matrix Renormalisation Group Algorithm for Anyonic Systems
• Simulation of braiding anyons using Matrix Product States
• Effective models of doped quantum ladders of non-Abelian anyons
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• Numerical simulation of non-abelian anyons
• Topological Insulating Phases of Non-Abelian Anyonic Chains
• Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands
• Phase transitions on a ladder of braided non-Abelian anyons
• Anyonic quasiparticles of hardcore anyons
• Twofold twist defect chains at criticality
• Studies of braided non-Abelian anyons using anyonic tensor networks
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling