Irreducibility of the Bloch Variety for Finite-Range Schr\"odinger Operators

TL;DR

This paper proves that the Bloch variety of finite-range Schrödinger operators with complex periodic potentials is irreducible across various lattice geometries, expanding understanding of spectral properties in quantum lattice models.

Contribution

It establishes the irreducibility of the Bloch variety for a broad class of lattice geometries and finite-range interactions, including complex potentials.

Findings

Bloch variety is irreducible for complex periodic potentials.

Irreducibility holds for various lattice geometries like triangular and extended Harper lattices.

Results apply in arbitrary dimensions.

Abstract

We study the Bloch variety of discrete Schr\"odinger 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.