Phase Diagram and Entanglement of two interacting topological Kitaev chains

Abstract

A superconducting wire described by a p-wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultra-cold atoms and Josephson junctions.

Final Version to be Published in Phys. Rev. B; 24 pages and 15 figures

References in corpus (23)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions
• Majorana edge states in interacting one-dimensional systems
• Topological Kondo effect with Majorana fermions
• Topological Superconductivity induced by Ferromagnetic Metal Chains
• Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
• Matrix Product State applications for the ALPS project
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• Topological States in a One-Dimensional Fermi Gas with Attractive Interactions
• Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires
• Diamagnetism of doped two-leg ladders and probing the nature of their commensurate phases
• Fluctuations and Entanglement spectrum in quantum Hall states
• Non-Fermi liquid manifold in a Majorana device

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