We investigate the non-Hermitian Kitaev chain with non-reciprocal hopping amplitudes and asymmetric superconducting pairing. We work out the symmetry structure of the model and show that particle-hole symmetry (PHS) is preserved throughout the entire parameter regime. As a consequence of PHS, the topological phase transition point of a finite open chain coincides with that of the periodic (infinite) system. By explicitly constructing the zero-energy wave functions (Majorana modes), we show that Majorana modes necessarily occur as reciprocal localization pairs accumulating on opposite boundaries, whose combined probability density exhibits an exact cancellation of the non-Hermitian skin effect for the zero energy modes. Excited states, by contrast, generically display skin-effect localization, with particle and hole components accumulating at opposite ends of the system. At the level of bulk topology, we further construct a $\mathbb{Z}_2$ topological invariant in restricted parameter regimes that correctly distinguishes the topological and trivial phases. Finally, we present the topological phase diagram of the non-Hermitian Kitaev chain across a broad range of complex parameters and delineate the associated phase boundaries.We investigate the non-Hermitian Kitaev chain with non-reciprocal hopping amplitudes and asymmetric superconducting pairing. We work out the symmetry structure of the model and show that particle-hole symmetry (PHS) is preserved throughout the entire parameter regime. As a consequence of PHS, the topological phase transition point of a finite open chain coincides with that of the periodic (infinite) system. By explicitly constructing the zero-energy wave functions (Majorana modes), we show that Majorana modes necessarily occur as reciprocal localization pairs accumulating on opposite boundaries, whose combined probability density exhibits an exact cancellation of the non-Hermitian skin effect for the zero energy modes. Excited states, by contrast, generically display skin-effect localization, with particle and hole components accumulating at opposite ends of the system. At the level of bulk topology, we further construct a $\mathbb{Z}_2$ topological invariant in restricted parameter regimes that correctly distinguishes the topological and trivial phases. Finally, we present the topological phase diagram of the non-Hermitian Kitaev chain across a broad range of complex parameters and delineate the associated phase boundaries.

cond-mat.mes-hallCross-listedarXiv:2601.00951Jan 6, 2026

Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes

Youguo Shi, Z. Song

Exact solutions for non-Hermitian quantum many-body systems are rare but may provide valuable insights into the interplay between Hermitian and non-Hermitian components. We report our investigation of a non-Hermitian variant of a $p$ -wave Kitaev chain by introducing staggered imbalanced pair creation and annihilation terms. We find that there exist fixed lines in the phase diagram, at which the ground state remains unchanged in the presence of a non-Hermitian term under the periodic boundary condition for a finite system. This allows the constancy of the topological index in the process of varying the balance strength at arbitrary rate, exhibiting the robustness of the topology for the non-Hermitian Kitaev chain under time-dependent perturbations. The underlying mechanism is investigated through the equivalent quantum spin system obtained by the Jordan-Wigner transformation for infinite chain. In addition, the exact solution shows that a resonant non-Hermitian impurity can induce a pair of zero modes in the corresponding Majorana lattice, which asymptotically approach the edge modes in the thermodynamic limit, manifesting the bulk-boundary correspondence. Numerical simulation is performed for the quench dynamics for the systems with slight deviation from the fixed lines to show the stability region in time. This work reveals the interplay between the pair creation and annihilation pairing processes.Exact solutions for non-Hermitian quantum many-body systems are rare but may provide valuable insights into the interplay between Hermitian and non-Hermitian components. We report our investigation of a non-Hermitian variant of a $p$-wave Kitaev chain by introducing staggered imbalanced pair creation and annihilation terms. We find that there exist fixed lines in the phase diagram, at which the ground state remains unchanged in the presence of a non-Hermitian term under the periodic boundary condition for a finite system. This allows the constancy of the topological index in the process of varying the balance strength at arbitrary rate, exhibiting the robustness of the topology for the non-Hermitian Kitaev chain under time-dependent perturbations. The underlying mechanism is investigated through the equivalent quantum spin system obtained by the Jordan-Wigner transformation for infinite chain. In addition, the exact solution shows that a resonant non-Hermitian impurity can induce a pair of zero modes in the corresponding Majorana lattice, which asymptotically approach the edge modes in the thermodynamic limit, manifesting the bulk-boundary correspondence. Numerical simulation is performed for the quench dynamics for the systems with slight deviation from the fixed lines to show the stability region in time. This work reveals the interplay between the pair creation and annihilation pairing processes.

arXiv:2305.00496Physical review. B./Physical review. BSep 15, 20231 citation

From Ising Model to Kitaev Chain

Kartik Chhajed

arXiv:2009.01078ResonanceNov 1, 20214 citations

\mathbb{Z}_2

topological invariant in restricted parameter regimes that correctly distinguishes the topological and trivial phases. Finally, we present the topological phase diagram of the non-Hermitian Kitaev chain across a broad range of complex parameters and delineate the associated phase boundaries.

p

-wave Kitaev chain by introducing staggered imbalanced pair creation and annihilation terms. We find that there exist fixed lines in the phase diagram, at which the ground state remains unchanged in the presence of a non-Hermitian term under the periodic boundary condition for a finite system. This allows the constancy of the topological index in the process of varying the balance strength at arbitrary rate, exhibiting the robustness of the topology for the non-Hermitian Kitaev chain under time-dependent perturbations. The underlying mechanism is investigated through the equivalent quantum spin system obtained by the Jordan-Wigner transformation for infinite chain. In addition, the exact solution shows that a resonant non-Hermitian impurity can induce a pair of zero modes in the corresponding Majorana lattice, which asymptotically approach the edge modes in the thermodynamic limit, manifesting the bulk-boundary correspondence. Numerical simulation is performed for the quench dynamics for the systems with slight deviation from the fixed lines to show the stability region in time. This work reveals the interplay between the pair creation and annihilation pairing processes.