Majorana Spin Liquids, Topology and Superconductivity in Ladders

Abstract

We theoretically address spin chain analogs of the Kitaev quantum spin model on the honeycomb lattice. The emergent quantum spin liquid phases or Anderson resonating valence bond (RVB) states can be understood, as an effective model, in terms of p-wave superconductivity and Majorana fermions. We derive a generalized phase diagram for the two-leg ladder system with tunable interaction strengths between chains allowing us to vary the shape of the lattice (from square to honeycomb ribbon or brickwall ladder). We evaluate the winding number associated with possible emergent (topological) gapless modes at the edges. In the Az phase, as a result of the emergent Z2 gauge fields and pi-flux ground state, one may build spin-1/2 (loop) qubit operators by analogy to the toric code. In addition, we show how the intermediate gapless B phase evolves in the generalized ladder model. For the brickwall ladder, the $B$ phase is reduced to one line, which is analyzed through perturbation theory in a rung tensor product states representation and bosonization. Finally, we show that doping with a few holes can result in the formation of hole pairs and leads to a mapping with the Su-Schrieffer-Heeger model in polyacetylene; a superconducting-insulating quantum phase transition for these hole pairs is accessible, as well as related topological properties.

25 pages, 10 figures, final version - to be published in PRB

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• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Quantum Entangled Fractional Topology and Curvatures
• Antiferromagnetic magnons from fractionalized excitations
• Spin dynamics of the generalized quantum spin compass chain
• Dynamical structure factor in the non-Abelian phase of the Kitaev honeycomb model in the presence of quenched disorder
• Engineering Quantum Spin Liquids and Many-Body Majorana States with a Driven Superconducting Box Circuit
• Spin liquid fingerprints in the thermal transport of a Kitaev-Heisenberg ladder
• Valence bond fluctuations in the Kitaev spin model
• Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
• Moiré pattern of spin liquid and Neel magnet in a Kitaev chain
• Competing phases and critical behavior in three coupled spinless Luttinger liquids
• Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions
• Emergent Quadrupolar Order in the Spin-$1/2$ Kitaev-Heisenberg Model
• Spinor Bose-Einstein condensates subject to current-density interactions