A Model for Topological p-wave Superconducting Wires with Disorder and Interactions
arXiv:2408.02105 · doi:10.1103/PhysRevB.111.075170
Abstract
We present a comprehensive theoretical study of interacting and disordered topological phases of coupled Kitaev wires, which may support further realistic applications of Majorana fermions. We develop a variety of analytical, mathematical and numerical methods for one and two-coupled wires, associated with a topological marker accessible from real-space correlation functions on the wire(s). We verify the stability of the topological superconducting phase and quantify disorder effects close to the quantum phase transitions, e.g. through two-point correlation functions or using a renormalization group (RG) analysis of disorder. We show for the first time that the double critical Ising (DCI) phase -- a fractional Majorana liquid characterized by a pair of half central charges and topological numbers -- is stabilized by strong interactions against disorder which respects the inversion symmetry between the wires (ie. parity conservation on each wire). In the presence of an inter-wire hopping term, the DCI phase turns into a protected topological phase with a bulk gap. We study the localization physics developing along the critical line for weaker interactions.
13 pages, 11 figures (+ Appendices)
References in corpus (42)
- Topological Insulators
- Unpaired Majorana fermions in quantum wires
- The density-matrix renormalization group in the age of matrix product states
- The density-matrix renormalization group
- New directions in the pursuit of Majorana fermions in solid state systems
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Topological quantum memory
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- The ITensor Software Library for Tensor Network Calculations
- The effects of interactions on the topological classification of free fermion systems
- Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
- Elastic Theory of pinned flux lattices
- Mapping topological order in coordinate space
- Realization of a minimal Kitaev chain in coupled quantum dots
- Entanglement Spectrum of a Disordered Topological Chern Insulator
- Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions
- A Short Introduction to Topological Quantum Computation
- Exact ground states and topological order in interacting Kitaev/Majorana chains
- Noise-resilient Edge Modes on a Chain of Superconducting Qubits
- Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions
- Majorana Fermions and Multiple Topological Phase Transition in Kitaev Ladder Topological Superconductors
- Competition of random and periodic potentials in interacting fermionic systems and classical equivalents: the Mott Glass
- Coupling-Matrix Approach to the Chern Number Calculation in Disordered Systems
- Cavity quantum electrodynamics with mesoscopic topological superconductors
- Density Matrix Renormalization Group for Dummies
- Braiding Majorana zero modes using quantum dots
- Direct cavity detection of Majorana pairs
- Phases of the two-band model of spinless fermions in one dimension
- Disorder effects on Majorana zero modes: Kitaev chain versus semiconductor nanowire
- Interacting Stochastic Topology and Mott Transition from Light Response
- Interaction-Driven Instabilities in the Random-Field XXZ Chain
- Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study
- Josephson effect in topological superconducting rings coupled to a microwave cavity
- Phase Diagram and Entanglement of two interacting topological Kitaev chains
- From Topological Superconductivity to Quantum Hall States in Coupled Wires
- Quantum Entangled Fractional Topology and Curvatures
- Topological and quantum critical properties of the interacting Majorana chain model
- Quantum memories with zero-energy Majorana modes and experimental constraints
- Kondo effect in a one dimensional d-wave superconductor
- Reshaping the Jaynes-Cummings ladder with Majorana bound states
- Critical Ising modes in low-dimensional Kondo insulators
- Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder