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.

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

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• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
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• 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
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• Strong and almost strong modes of Floquet spin chains in Krylov subspaces
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