Surface modes and chiral symmetry (Wilson Fermions in a box)

TL;DR

This paper explores surface states in lattice models with Wilson fermions, linking their emergence to band gap transitions and chiral symmetry, providing a Hamiltonian perspective on these phenomena.

Contribution

It introduces a Hamiltonian framework for understanding surface modes in Wilson fermion lattice models, highlighting their relation to band gap dynamics and chiral symmetry.

Findings

Surface modes appear when the Wilson hopping parameter exceeds a critical value.

Surface states are associated with the closing and reopening of the band gap.

The work connects surface states to historical Shockley surface state concepts.

Abstract

We give a Hamiltonian discussion of surface states in an extra dimension as a basis for chiral fermions in lattice models. Such modes appear with the Wilson fermion action when the hopping parameter exceeds a critical value. The association of such states with the closing and reopening of a band gap was noted by Shockley in 1939. Poster presented by Michael Creutz at Lattice 93. Uuencoded compressed postscript file.