Osamu Fukushima

Higher-Form Symmetry and Eigenstate Thermalization Hypothesis (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Nature Singapore
• Seitenzahl: 75
• Erscheinungstermin: 11. April 2025
• Englisch
• ISBN-13: 9789819616435
• Artikelnr.: 73849435

Autorenporträt

Osamu Fukushima is a theoretical physicist specializing in high-energy physics, quantum field theory, and integrable field theories. He is currently a special postdoctoral researcher (SPDR) at RIKEN iTHEMS. His primary research interests include non-equilibrium quantum dynamics and exotic phenomena in quantum field theories. He received his Bachelor of Science in physics and Ph.D. in Science from Kyoto University in 2019 and 2024, respectively. From 2021 to 2024, he was awarded a research fellowship (DC1) by the Japan Society for the Promotion of Science (JSPS).

Inhaltsangabe

.- 1 Introduction.

.- 2 Thermalization in isolated quantum systems.

.- 3 Violation of the ETH in QFTs with higher-form symmetry.

.- 4 Effects of projective phase on the ETH.

.- 5 Conclusion and discussion.

.- 6 Appendices.