# Non-Hermitian Topological Invariants in Real Space

## TL;DR

This paper introduces a real-space method for defining topological invariants in non-Hermitian systems, enabling straightforward analysis of their topology even with the non-Hermitian skin effect.

## Contribution

It presents a novel real-space construction of non-Hermitian topological invariants, simplifying the determination of topology in complex non-Hermitian models.

## Key findings

- Efficiently computes topological invariants in non-Hermitian models.
- Provides a dual perspective to non-Bloch band theory.
- Demonstrates applicability to various non-Hermitian systems.

## Abstract

The topology of non-Hermitian systems is drastically shaped by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence and non-Bloch band theory. The essential part in formulations of bulk-boundary correspondence is a general and computable definition of topological invariants. In this paper, we introduce a construction of non-Hermitian topological invariants based directly on real-space wavefunctions, which provides a general and straightforward approach for determining non-Hermitian topology. As an illustration, we apply this formulation to several representative models of non-Hermitian systems, efficiently obtaining their topological invariants in the presence of non-Hermitian skin effect. Our formulation also provides a dual picture of the non-Bloch band theory based on the generalized Brillouin zone, offering a unique perspective of bulk-boundary correspondence.