03854nam 22006135 450 991099649500332120250411151520.09789819616435981961643310.1007/978-981-96-1643-5(CKB)38429305600041(DE-He213)978-981-96-1643-5(MiAaPQ)EBC32007522(Au-PeEL)EBL32007522(EXLCZ)993842930560004120250411d2025 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierHigher-Form Symmetry and Eigenstate Thermalization Hypothesis /by Osamu Fukushima1st ed. 2025.Singapore :Springer Nature Singapore :Imprint: Springer,2025.1 online resource (XIV, 75 p. 14 illus., 13 illus. in color.) Springer Theses, Recognizing Outstanding Ph.D. Research,2190-50619789819616428 9819616425 -- 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.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.Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5061Quantum theoryStatistical physicsParticles (Nuclear physics)Quantum field theoryFundamental concepts and interpretations of QMStatistical PhysicsElementary Particles, Quantum Field TheoryQuantum theory.Statistical physics.Particles (Nuclear physics)Quantum field theory.Fundamental concepts and interpretations of QM.Statistical Physics.Elementary Particles, Quantum Field Theory.530.12Fukushima Osamuauthttp://id.loc.gov/vocabulary/relators/aut474853MiAaPQMiAaPQMiAaPQBOOK9910996495003321Higher-Form Symmetry and Eigenstate Thermalization Hypothesis4375205UNINA