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

TL;DR

This paper investigates how entanglement spectrum dynamics can identify topological phase transitions in a long-range Kitaev chain, revealing new insights into the role of long-range interactions and quench protocols.

Contribution

It introduces a method to characterize topological phase transitions through entanglement-spectrum crossings in long-range superconducting models, extending previous short-range analyses.

Findings

Entanglement-spectrum crossings signal topological phase transitions.

Long-range interactions affect the stability and detection of TPTs.

A criterion based on the lowest upper-half entanglement-spectrum value for diagnosing TPTs.

Abstract

We study the quench dynamics of entanglement spectra in the Kitaev chain with variable-range pairing quantified by power-law decay rate $\alpha$. 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 ($\alpha$ > 1) or long-range ($\alpha$ < 1) sector. Properties of entanglement-spectrum dynamics are revealed for the quench protocols in the long-range sector or with $\alpha$ 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.