Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring

Abstract

On a ring, a single Jordan-Wigner transformation between the Kitaev model and the spin model suffers redundant degrees of freedom. However, we can establish an exact quaternary Jordan-Wigner mapping involving two Kitaev rings and two spin rings with periodic or antiperiodic boundary conditions. This mapping facilitates us to demonstrate exactly how a topological extended-kink (TEK) phase develops in the interacting Kitaev ring with odd number of lattice sites. The emergence of this new phase is attributed to the effect of geometrical ring frustration. Unlike the usual topological phases protected by energy gap in noninteracting systems, the TEK phase is gapless. And because the spectra of low energy excitations are quadratic, the specific heat per site approaches a half of Boltzmann constant near absolute zero temperature. More interestingly, the ground state is unique, immune to spontaneous symmetry breaking. It exhibits a long-range correlation function with a nonlocal factor, but no local order parameter can be defined. As a concomitant effect, a special kind of localized kink zero mode (KZM) takes place if we introduce a type of bond defect. We also show that the KZM is robust against moderate disorders.

arXiv comment11 pages, 9 figures

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• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Ring-Frustrated Non-Hermitian $XY$ Model
• Impurity-driven transitions in frustrated quantum Ising ring
• Quantum cluster kink and ring frustration