Softening of Majorana edge states by long-range couplings
arXiv:2301.12514 · doi:10.1103/PhysRevB.107.235146
Abstract
The inclusion of long-range couplings in the Kitaev chain is shown to modify the universal scaling of topological states close to the critical point. By means of the scattering approach, we prove that the Majorana states \textit{soften}, becoming increasingly delocalised at a universal rate which is only determined by the interaction range. This edge mechanism can be related to a change in the value of the bulk topological index at criticality, upon careful redefinition of the latter. The critical point turns out to be topologically akin to the trivial phase rather than interpolating between the two phases. Our treatment moreover showcases how various topological aspects of quantum models can be investigated analytically.
arXiv comment7 + 5 pages (main body + appendices), 3 figures
References in corpus (57)
- Fault-tolerant quantum computation by anyons
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Non-Abelian Anyons and Topological Quantum Computation
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- Unpaired Majorana fermions in quantum wires
- Quantum Machine Learning
- Classification of topological quantum matter with symmetries
- New directions in the pursuit of Majorana fermions in solid state systems
- Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
- Circuit Quantum Electrodynamics
- A generic new platform for topological quantum computation using semiconductor heterostructures
- Periodic table for topological insulators and superconductors
- Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
- Non-Abelian statistics and topological quantum information processing in 1D wire networks
- Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
- Cold atoms in cavity-generated dynamical optical potentials
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Demonstration of a small programmable quantum computer with atomic qubits
- Entanglement-free Heisenberg-limited phase estimation
- Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
- Quantum Data Fitting
- Milestones toward Majorana-based quantum computing
- Dipolar physics: A review of experiments with magnetic quantum gases
- Rydberg atom quantum technologies
- Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
- Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
- Topological Quantum Computation Based on Chiral Majorana Fermions
- Realization of a minimal Kitaev chain in coupled quantum dots
- Quantum Computation Using Vortices and Majorana Zero Modes of a + Superfluid of Fermionic Cold Atoms
- Efficient Networks for Quantum Factoring
- Bulk-edge correspondence for two-dimensional topological insulators
- Kitaev chains with long-range pairing
- Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
- Programmable Interactions and Emergent Geometry in an Atomic Array
- Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
- Topology and edge modes in quantum critical chains
- Topological Massive Dirac Edge Modes and Long-Range Superconducting Hamiltonians
- Extended Kitaev chain with longer-range hopping and pairing
- Floquet engineering of long-range p-wave superconductivity
- Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
- Critical Phenomena and Kibble-Zurek Scaling in the Long-Range Quantum Ising Chain
- Simulating the dynamics of braiding of Majorana zero modes using an IBM quantum computer
- Topological Quantum Liquids with Long-Range Couplings
- Particle-Hole Symmetries in Condensed Matter
- Edge states of the long-range Kitaev chain: an analytical study
- Singular dynamics and emergence of nonlocality in long-range quantum models
- Disorder effects on Majorana zero modes: Kitaev chain versus semiconductor nanowire
- Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
- Universal dynamical scaling of long-range topological superconductors
- Current transport properties and phase diagram of a Kitaev chain with long-range pairing
- Equivalence of topological and scattering approaches to quantum pumping
- Floquet engineering of long-range p-wave superconductivity: Beyond the high-frequency limit
- Zero modes of the Kitaev chain with phase-gradients and longer range couplings
- Scattering approach to Anderson localisation
- Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits
- Majorana orthogonal transformation and Majorana zero modes in free fermionic systems
- A Unified Theory of Quasibound States
Cited by in corpus (4)
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
- Strange correlators for topological quantum systems from bulk-boundary correspondence
- Electrical, thermal and thermoelectric transport in open long-range Kitaev chain
- Dynamics of Majorana zero modes across hybrid Kitaev chain