Entanglement Signature of Hinge Arcs, Fermi Arcs, and Crystalline Symmetry Protection in Higher-Order Weyl Semimetals

TL;DR

This paper explores how entanglement spectrum and wavefunctions can be used to identify boundary states and symmetry protections in higher-order Weyl semimetals, advancing understanding of gapless topological phases.

Contribution

It introduces a comprehensive method combining entanglement spectrum and wavefunctions to detect boundary states and symmetry protections in gapless topological phases like HOWSMs.

Findings

Both hinge arcs and Fermi arcs contribute to 1/2 modes in entanglement spectrum.

Entanglement wavefunctions localize on hinges and surfaces, respectively.

Minimal crystalline symmetries protecting boundary states are identified through symmetry-breaking partitions.

Abstract

The existence of $1/2$ modes in the entanglement spectrum (ES) has been shown to be a powerful quantum-informative signature of boundary states of gapped topological phases of matter, e.g., topological insulators and topological superconductors, where the finite bulk gap allows us to establish a crystal-clear correspondence between $1/2$ modes and boundary states. Here we investigate the recently proposed higher-order Weyl semimetals (HOWSM), where bulk supports gapless higher-order Weyl nodes and boundary supports hinge arcs and Fermi arcs. We find that the aim of unambiguously identifying higher-order boundary states ultimately drives us to make full use of eigen quantities of the entanglement Hamiltonian: ES as well as Schmidt vectors (entanglement wavefunctions, abbr. EWF). We demonstrate that, while both hinge arcs and Fermi arcs contribute to $1/2$ modes, the EWFs corresponding to hinge arcs and Fermi arcs are respectively localized on the virtual hinges and surfaces of the partition. Besides, by means of various symmetry-breaking partitions, we can identify the minimal crystalline symmetries that protect boundary states. Therefore, for gapless topological phases such as HOWSMs, we can combine ES and EWF to universally identify boundary states and potential symmetry requirement. While HOWSMs are prototypical examples of gapless phases, our work sheds light on general theory of entanglement signature in gapless topological phases of matter.