Irreducibility of the Bloch Variety for Finite-Range Schrödinger Operators

Abstract

We study the Bloch variety of discrete Schrödinger operators associated with a complex periodic potential and a general finite-range interaction, showing that the Bloch variety is irreducible for a wide class of lattice geometries in arbitrary dimension. Examples include the triangular lattice and the extended Harper lattice.

References in corpus (5)

• Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues
• Reducible Fermi surface for multi-layer quantum graphs including stacked graphene
• Topics on Fermi varieties of discrete periodic Schrödinger operators
• Fermi isospectrality for discrete periodic Schrodinger operators
• Critical points of discrete periodic operators

Cited by in corpus (5)

• Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues
• Topics on Fermi varieties of discrete periodic Schrödinger operators
• Fermi isospectrality of discrete periodic Schrödinger operators with separable potentials on ${\mathbb{Z}}^2$
• Fermi isospectrality for discrete periodic Schrodinger operators
• The curious spectra and dynamics of non-locally finite crystals