Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain

Abstract

What distinguishes trivial from topological superluids in interacting many-body systems where the number of particles is conserved? Building on a class of integrable pairing Hamiltonians, we present a number-conserving, interacting variation of the Kitaev model, the Richardson-Gaudin-Kitaev chain, that remains exactly solvable for periodic and antiperiodic boundary conditions. Our model allows us to identify fermionic parity switches that distinctively characterize topological superconductivity in interacting many-body systems. Although the Majorana zero-modes in this model have only a power-law confinement, we may still define many-body Majorana operators by tuning the flux to a fermion parity switch. We derive a closed-form expression for an interacting topological invariant and show that the transition away from the topological phase is of third order.

arXiv comment5 pages, 2 figures

References in corpus (43)

• Topological Insulators
• Topological insulators and superconductors
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Search for Majorana fermions in superconductors
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Majorana fermions in chains of magnetic atoms on a superconductor
• Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures
• Topological superconducting phase in helical Shiba chains
• Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
• Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Quantized conductance at the Majorana phase transition in a disordered superconducting wire
• Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors
• Kitaev chains with long-range pairing
• Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
• Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
• Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order
• Tunneling Spectroscopy of Quasiparticle Bound States in a Spinful Josephson Junction
• A Class of Exactly Solvable Pairing Models
• Inducing time reversal invariant topological superconductivity and fermion parity pumping in quantum wires
• Coulomb stability of the 4π-periodic Josephson effect of Majorana fermions
• A number conserving theory for topologically protected degeneracy in one-dimensional fermions
• Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium
• Time-Reversal Invariant Topological Superconductivity Induced by Repulsive Interactions in Quantum Wires
• Majorana Edge States in Interacting Two-chain Ladders of Fermions
• Strongly interacting Majorana modes in an array of Josephson junctions
• Integrable model for interacting electrons in metallic grains
• Quantum phase diagram of the integrable p_x+ip_y fermionic superfluid
• Shiba impurity bound states as a probe of topological superconductivity and Fermion parity changing quantum phase transitions
• BCS-to-BEC crossover from the exact BCS solution
• Quantum Phase Transition in the BCS-to-BEC Evolution of p-wave Fermi Gases
• Exactly solvable pairing model for superconductors with a p+ip-wave symmetry
• Parity measurement in topological Josephson junctions
• Wigner-Poisson statistics of topological transitions in a Josephson junction
• Coulomb interaction effects on the Majorana states in quantum wires
• Integrable two-channel p_x+ip_y-wave superfluid model
• Thermal conductance as a probe of the non-local order parameter for a topological superconductor with gauge fluctuations

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