Edge State, Entanglement Entropy Spectra and Critical Hopping Coupling of Anisotropic Honeycomb Lattice

TL;DR

This paper investigates how Berry phase, entanglement spectra, and edge states in an anisotropic honeycomb lattice are interconnected, revealing critical hopping couplings that induce zero-energy states with potential topological significance.

Contribution

It demonstrates the dependence of Berry phase on hopping couplings and system shape, and links entanglement spectra to zero-energy edge states in anisotropic honeycomb lattices.

Findings

Maximal entangled states correspond to zero-energy edge states.

Critical hopping couplings induce pairwise zero-energy states.

Berry phase depends on system shape and hopping parameters.

Abstract

For a bipartite honeycomb lattice, we show that the Berry phase depends not only on the shape of the system but also on the hopping couplings. Using the entanglement entropy spectra obtained by diagonalizing the block Green's function matrices, the maximal entangled state with the eigenvalue $\lambda_m=1/2$ of the reduced density matrix is shown to have one-to-one correspondence to the zero energy states of the lattice with open boundaries, which depends on the Berry phase. For the systems with finite bearded edges along $x$-direction we find critical hopping couplings: the maximal entangled states (zero-energy states) appear pair by pair if one increases the hopping coupling $h$ over the critical couplings $h_c$s.