# Non-Bloch Band Theory of Non-Hermitian Systems

## TL;DR

This paper develops a generalized Bloch band theory for non-Hermitian systems, enabling the calculation of band structures and topological properties in open boundary conditions, extending traditional band theory to non-Hermitian physics.

## Contribution

It introduces a non-Hermitian Bloch band theory, defining a new Brillouin zone and linking bulk topological invariants to edge states in non-Hermitian systems.

## Key findings

- Defined a non-Hermitian Brillouin zone.
- Reproduced open-boundary band structures from continuum bands.
- Established bulk-edge correspondence via winding number.

## Abstract

In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries. In this paper, we establish a generalized Bloch band theory in one-dimensional spatially periodic tight-binding models. We show how to define the Brillouin zone in non-Hermitian systems. From this Brillouin zone, one can calculate continuum bands, which reproduce the band structure in an open chain. As an example, we apply our theory to the non-Hermitian Su-Schrieffer-Heeger model. We also show the bulk-edge correspondence between the winding number and existence of the topological edge states.