Statistical translation invariance protects a topological insulator from interactions

Abstract

We investigate the effect of interactions on the stability of a disordered, two-dimensional topological insulator realized as an array of nanowires or chains of magnetic atoms on a superconducting substrate. The Majorana zero-energy modes present at the ends of the wires overlap, forming a dispersive edge mode with thermal conductance determined by the central charge $c$ of the low-energy effective field theory of the edge. We show numerically that, in the presence of disorder, the $c=1/2$ Majorana edge mode remains delocalized up to extremely strong attractive interactions, while repulsive interactions drive a transition to a $c=3/2$ edge phase localized by disorder. The absence of localization for strong attractive interactions is explained by a self-duality symmetry of the statistical ensemble of disorder configurations and of the edge interactions, originating from translation invariance on the length scale of the underlying mesoscopic array.

5+2 pages, 8 figures

References in corpus (13)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Scaling of entanglement support for Matrix Product States
• Chiral P-Wave Order in Sr_2RuO_4
• Low-energy effective theory in the bulk for transport in a topological phase
• Quantum Thermal Hall Effect in a Time-Reversal-Symmetry-Broken Topological Superconductor in Two Dimensions : Approach From Bulk Calculations
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Strongly interacting Majorana fermions
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
• Bimodal conductance distribution of Kitaev edge modes in topological superconductors
• Increasing entanglement through engineered disorder in the random Ising chain

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• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
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• Majorana Loop Models for Measurement-Only Quantum Circuits
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Majorana-Hubbard model on the square lattice
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• Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains
• Exact ground states for interacting Kitaev chains
• Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladder
• Majorana-Hubbard model on the honeycomb lattice
• Topologically protected charge transfer along the edge of a chiral $\text{p}$-wave superconductor
• Disorder and interaction in chiral chains: Majoranas vs complex fermions
• Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• Topological and quantum critical properties of the interacting Majorana chain model
• Tricritical Ising phase transition in two-ladder Majorana fermion lattice
• Phase diagrams of Majorana-Hubbard ladders
• Equivalence of Topological Insulators and Superconductors
• Counterdiabatic optimized driving in quantum phase sensitive models
• Simulating Floquet topological phases in static systems
• Classical impurities and boundary Majorana zero modes in quantum chains
• Majorana stripe order on the surface of a three-dimensional topological insulator
• Resilient infinite randomness criticality for a disordered chain of interacting Majorana fermions
• Transport properties of an interacting Majorana chain
• Practical new platform for interaction-enabled topological phases
• Universal Characterization of Quantum Many-Body States through Local Information
• Critical properties of the Majorana chain with competing interactions
• Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder
• Nematic order in topological SYK models