Exact ground states for interacting Kitaev chains

Abstract

We introduce a frustration-free, one-dimensional model of spinless fermions with hopping, p-wave superconducting pairing and alternating chemical potentials. The model possesses two exactly degenerate ground states even for finite system sizes. We present analytical results for the strong Majorana zero modes, the phase diagram and the topological order. Furthermore, we generalise our results to include interactions.

corrected typo in (32) and (33), added clarifying remarks in App. D

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• The density-matrix renormalization group in the age of matrix product states
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
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• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Exact solutions and topological phase diagram in interacting dimerized Kitaev topological superconductors
• Spin chains with dynamical lattice supersymmetry
• Factorization and criticality in finite XXZ systems of arbitrary spin
• Reentrant Topological Phase Transition in a Bridging Model between Kitaev and Haldane Chains

Cited by in corpus (20)

• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $\eta$ pairing, weak ergodicity breaking, and partial integrability
• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
• Exact solutions of few-magnon problems in the spin-$S$ periodic XXZ chain
• Spontaneous breaking of U(1) symmetry at zero temperature in one dimension
• Quadratic dispersion relations in gapless frustration-free systems
• Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring
• On the critical finite-size gap scaling for frustration-free Hamiltonians
• Exact weak bosonic zero modes in a spin/fermion chain
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Topological phases in the presence of disorder and longer-range couplings
• Brick Wall Quantum Circuits with Global Fermionic Symmetry
• Frustration-free free fermions
• Frustration-free free fermions and beyond
• Interrelations among frustration-free models via Witten's conjugation
• Quasi-local Frustration-Free Free Fermions
• Strong and almost strong modes of Floquet spin chains in Krylov subspaces
• Phase diagram of an extended parafermion chain
• Exact steady states and fragmentation-induced relaxation in the no-passing asymmetric simple exclusion process