Over the past twenty-five years, mathematical concepts associated with geometric phases have come to occupy a central place in our modern understanding of the physics of electrons in solids. These ‘Berry phases’ describe the global phase acquired by a quantum state as the Hamiltonian is changed. Beginning at an elementary level, this book provides a pedagogical introduction to the important role of Berry phases and curvatures, and outlines their great influence upon many key properties of electrons in solids, including electric polarization, anomalous Hall conductivity, and the nature of the topological insulating state. It focuses on drawing connections between physical concepts and provides a solid framework for their integration, enabling researchers and students to explore and develop links to related fields. Computational examples and exercises throughout provide an added dimension to the book, giving readers the opportunity to explore the central concepts in a practical and engaging way.
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- Introduction to Berry Phases in Quantum Physics: This book offers a pedagogical overview of Berry phases, emphasizing their importance in understanding electron behavior in solids and their influence on properties like electric polarization and topological states.
What are Berry phases and why are they important in quantum physics?
Berry phases are global phases acquired by a quantum state as the Hamiltonian of a system is varied. They are important because they play a central role in understanding the behavior of electrons in solids, influencing properties such as electric polarization, anomalous Hall conductivity, and the topological insulating state.
