Tight-Binding realization of non-abelian gauge fields: singular spectra
and wave confinement
- URL: http://arxiv.org/abs/2106.05417v1
- Date: Wed, 9 Jun 2021 22:15:24 GMT
- Title: Tight-Binding realization of non-abelian gauge fields: singular spectra
and wave confinement
- Authors: Y. Hern\'andez-Espinosa and E. Sadurn\'i
- Abstract summary: We present a geometric construction of a lattice that emulates the action of a gauge field on a fermion.
The emulation covers both abelian and non-abelian gauge fields.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present a geometric construction of a lattice that emulates the action of
a gauge field on a fermion. The construction consists of a square lattice made
of polymeric sites, where all clustered atoms are identical and represented by
potential wells or resonators supporting one bound state. The emulation covers
both abelian and non-abelian gauge fields. In the former case, Hofstadter's
butterfly is reproduced by means of a chain made of rotating dimers, subject to
periodic boundary conditions parallel to the chain. A rigorous map between this
model and Harper's Hamiltonian is derived. In the non-abelian case, band mixing
and wave confinement are obtained by interband coupling using SU(2) as an
internal group, \ie the effects are due to non-commutability of field
components. A colored model with SU(3) made of trimers is also studied, finding
thereby the appearance of flat bands in special configurations. This work
constitutes the first all-geometric emulation of the Peierls substitution, and
is valid for many types of waves.
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