Curved domain-wall fermions

Abstract

We consider fermion systems on a square lattice with a mass term having a curved domain-wall. Similarly to the conventional flat domain-wall fermions, massless and chiral edge states appear on the wall. In the cases of $S^1$ and $S^2$ domain-walls embedded into flat hypercubic lattices, we find that these edge modes feel gravity through the induced Spin or Spin${}^c$ connections. The gravitational effect is encoded in the Dirac eigenvalue spectrum as a gap from zero. In the standard continuum extrapolation of the square lattice, we find a good agreement with the analytic prediction in the continuum theory. We also find that the rotational symmetry of the edge modes is automatically recovered in the continuum limit.

24 pages, 12 figures, minor corrections, to appear in PTEP

References in corpus (7)

• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Quantum Gravity on the Lattice
• Spherical topological insulator
• Persistent and radiation-induced currents in distorted quantum rings
• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
• Spin connection and boundary states in a topological insulator
• Dirac operator on the Riemann sphere

Cited by in corpus (1)

• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration