Topological Phase Transition of Non‐Hermitian Crosslinked Chain

The contents of topological classification of matter are enriched by non‐Hermiticity, such as exceptional points, bulk‐edge correspondence, and skin effects. Physically, gain and loss can be introduced by imaginary on‐site potentials of lattice Hamiltonians, and the topological phase transition for a cross‐linked chain in the presence of such non‐Hermiticity is investigated. The topological phase diagram in terms of a winding number is obtained analytically with phase boundaries coinciding with the surfaces of exceptional points. The topologically original edge states with distribution mainly at the joints between domains of different phases are protected even for long chains. The non‐Hermitian topological feature can also be reflected by vortex structures in the vector fields of complex eigenenergies, expected values of Pauli matrices, and trajectories of these quantities. This model may be implemented in coupled photonic crystals, fermions trapped in optical lattice, or non‐Hermitian electrical‐circuit lattices, and the edge states are immune to various kinds of disorders until topological phase transition occurs. This work gives insight into the influence of non‐Hermiticity on topological phase of matter. The topological phase transition of a crosslinked chain with balanced gain and loss is investigated. The exceptional points separate different topological phases which coincides with the behavior of eigenenergies and expectation values. The balanced gain and loss make the eigenstates locate on fractional sites, and the edge states behave tenaciously against various disorders until topological phase transition occur.