Non-Bloch Band Theory of Non-Hermitian Systems

The book introduces a non-Bloch band theory for non-Hermitian systems,which produces an energy spectrum with unique features such as topological edge states and a topological semimetal phase. It also reveals relationships between non-Bloch waves and non-Hermitian topology.

Format: Paperback / softback
Length: 92 pages
Publication date: 24 April 2023
Publisher: Springer Verlag, Singapore

This book is a groundbreaking exploration into the realm of non-Hermitian physics, where it constructs a novel non-Bloch band theory to understand the physics described by non-Hermitian Hamiltonians. In the context of non-Hermitian crystals, the author introduces this theory, which yields an energy spectrum in the limit of a large system size. This energy spectrum is calculated using a generalized Brillouin zone, which takes into account the complex Bloch wave number. Interestingly, while a generalized Brillouin zone in Hermitian systems forms a unit circle on a complex plane, it becomes a circle with cusps in non-Hermitian systems. These unique features of the generalized Brillouin zone unlock remarkable phenomena that are peculiar to non-Hermitian systems.

Furthermore, the author delves into the rich aspects of non-Hermitian physics through the lens of the non-Bloch band theory. Firstly, a topological invariant defined by the generalized Brillouin zone implies the emergence of topological edge states. These edge states are unique to non-Hermitian systems and are characterized by their behavior at the boundaries of the Brillouin zone. Secondly, the book introduces a topological semimetal phase with exceptional points, which is a hallmark of non-Hermitian systems. This phase arises due to the deformation of the generalized Brillouin zone by changes in the system parameters, resulting in a novel phase of matter with extraordinary properties. Thirdly, the author reveals a fascinating relationship between the non-Bloch waves and non-Hermitian topology. By studying the behavior of these waves, the author uncovers new insights into the complex interplay between topology and quantum mechanics, shedding light on the underlying principles governing non-Hermitian systems.

This book is a must-read for anyone interested in advancing their understanding of non-Hermitian physics and its applications in various fields, including quantum computing, materials science, and condensed matter physics. With its comprehensive and insightful approach, it provides a solid foundation for future research and innovation in this rapidly evolving field.

Weight: 180g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811918605
Edition number: 1st ed. 2022