Higher-Form Symmetry and Eigenstate Thermalization Hypothesis
The eigenstate thermalization hypothesis (ETH) provides a successful framework for understanding thermalization in isolated quantum systems. While extensive numerical and theoretical studies support ETH as a key mechanism for thermalization, determining whether specific systems satisfy ETH analytica...
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| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Singapore :
Springer Nature Singapore : Imprint: Springer,
2025.
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| Ausgabe: | 1st ed. 2025. |
| Schriftenreihe: | Springer Theses, Recognizing Outstanding Ph.D. Research,
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| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.1007/978-981-96-1643-5 |
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| Zusammenfassung: | The eigenstate thermalization hypothesis (ETH) provides a successful framework for understanding thermalization in isolated quantum systems. While extensive numerical and theoretical studies support ETH as a key mechanism for thermalization, determining whether specific systems satisfy ETH analytically remains a challenge. In quantum many-body systems and quantum field theories, ETH violations signal nontrivial thermalization processes and are gaining attention. This book explores how higher-form symmetries affect thermalization dynamics in isolated quantum systems. It analytically shows that a p-form symmetry in a $(d+1)$-dimensional quantum field theory can cause ETH breakdown for certain nontrivial $(d-p)$-dimensional observables. For discrete higher-form symmetries (i.e., $p\geq 1$), thermalization fails for observables that are non-local yet much smaller than the system size, despite the absence of local conserved quantities. Numerical evidence is provided for the $(2+1)$-dimensional $\mathbb{Z}_2$ lattice gauge theory, where local observables thermalize, but non-local ones, such as those exciting a magnetic dipole, relax to a generalized Gibbs ensemble incorporating the $\mathbb{Z}_2$ 1-form symmetry. The ETH violation mechanism here involves the mixing of symmetry sectors within an energy shell—a rather difficult condition to verify. To address this, the book introduces a projective phase framework for $\mathbb{Z}_N$-symmetric theories, supported by numerical analyses of spin chains and lattice gauge theories. |
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| Beschreibung: | XIV, 75 p. 14 illus., 13 illus. in color. online resource. |
| ISBN: | 9789819616435 |
| ISSN: | 2190-5061 |
| DOI: | 10.1007/978-981-96-1643-5 |