Quench dynamics of entanglement spectrum and topological superconducting phases in a long-range Hamiltonian

We study the quench dynamics of entanglement spectra in the Kitaev chain with variable-range pairing quantified by power-law decay rate α. Considering the post-quench Hamiltonians with flat bands, we demonstrate that the presence of entanglement-spectrum crossings during its dynamics is able to characterize the topological phase transitions (TPTs) in both short-range (α > 1) or long-range (α < 1) sector. Properties of entanglement-spectrum dynamics are revealed for the quench protocols in the long-range sector or with α as the quench parameter. In particular, when the lowest upper-half entanglement-spectrum value of the initial Hamiltonian is smaller than the final one, the TPTs can also be diagnosed by the difference between the lowest two upper-half entanglement-spectrum values if the halfway winding number is not equal to that of the initial Hamiltonian. Moreover, we discuss the stability of characterizing the TPTs via entanglement-spectrum crossings against energy dispersion in the long-range model.