Topological Gapped Phases of Matter: Band Theory to Fractional Chern Insulators

Jonah Herzog-Arbeitman; Bogdan Andrei Bernevig

doi:10.1016/B978-0-323-95703-8.00036-7

Topological Gapped Phases of Matter: Band Theory to Fractional Chern Insulators

Jonah Herzog-Arbeitman
, Bogdan Andrei Bernevig

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Topology has driven the prediction and classification of quantum states of matter in the last several decades. Here we review its basic formulation from the perspective of band theory, space group symmetry, and quantum geometry. Our aim is to convey the conceptual development of the field from the current vantage point of topological materials, along with practical formulae, example models, and an overview of ongoing research.

Original language	English (US)
Title of host publication	Encyclopedia of Mathematical Physics, Second Edition
Subtitle of host publication	Volumes 1-5
Publisher	Elsevier
Pages	V1:1-V1:16
Volume	1-5
ISBN (Electronic)	9780323957069
ISBN (Print)	9780323957038
DOIs	https://doi.org/10.1016/B978-0-323-95703-8.00036-7
State	Published - Jan 1 2024

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Band theory
Classification
Fractional chern insulators.
Many-body topology
Quantum geometry
Space group symmetry
Topological materials
Topological quantum field theory
Topology

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10.1016/B978-0-323-95703-8.00036-7

Cite this

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abstract = "Topology has driven the prediction and classification of quantum states of matter in the last several decades. Here we review its basic formulation from the perspective of band theory, space group symmetry, and quantum geometry. Our aim is to convey the conceptual development of the field from the current vantage point of topological materials, along with practical formulae, example models, and an overview of ongoing research.",

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AB - Topology has driven the prediction and classification of quantum states of matter in the last several decades. Here we review its basic formulation from the perspective of band theory, space group symmetry, and quantum geometry. Our aim is to convey the conceptual development of the field from the current vantage point of topological materials, along with practical formulae, example models, and an overview of ongoing research.

KW - Band theory

KW - Classification

KW - Fractional chern insulators.

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KW - Quantum geometry

KW - Space group symmetry

KW - Topological materials

KW - Topological quantum field theory

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ER -

Topological Gapped Phases of Matter: Band Theory to Fractional Chern Insulators

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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