LEADER 03854nam 22006135 450 001 9910996495003321 005 20250411151520.0 010 $a9789819616435 010 $a9819616433 024 7 $a10.1007/978-981-96-1643-5 035 $a(CKB)38429305600041 035 $a(DE-He213)978-981-96-1643-5 035 $a(MiAaPQ)EBC32007522 035 $a(Au-PeEL)EBL32007522 035 $a(EXLCZ)9938429305600041 100 $a20250411d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHigher-Form Symmetry and Eigenstate Thermalization Hypothesis /$fby Osamu Fukushima 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (XIV, 75 p. 14 illus., 13 illus. in color.) 225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5061 311 08$a9789819616428 311 08$a9819616425 327 $a -- 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. 330 $aThe 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. 410 0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5061 606 $aQuantum theory 606 $aStatistical physics 606 $aParticles (Nuclear physics) 606 $aQuantum field theory 606 $aFundamental concepts and interpretations of QM 606 $aStatistical Physics 606 $aElementary Particles, Quantum Field Theory 615 0$aQuantum theory. 615 0$aStatistical physics. 615 0$aParticles (Nuclear physics) 615 0$aQuantum field theory. 615 14$aFundamental concepts and interpretations of QM. 615 24$aStatistical Physics. 615 24$aElementary Particles, Quantum Field Theory. 676 $a530.12 700 $aFukushima$b Osamu$4aut$4http://id.loc.gov/vocabulary/relators/aut$0474853 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910996495003321 996 $aHigher-Form Symmetry and Eigenstate Thermalization Hypothesis$94375205 997 $aUNINA LEADER 01313nam0 22003493i 450 001 MIL0073238 005 20251003044222.0 100 $a20080213d1979 ||||0itac50 ba 101 | $aeng 102 $anl 181 1$6z01$ai $bxxxe 182 1$6z01$an 183 1$6z01$anc$2RDAcarrier 200 1 $aCombinatorial complexes$eˆa ‰mathematical theory of algorithms$fPeter H. Sellers 210 $aDordrecht [etc.]$cD. Reidel$dc1979 215 $aXV, 184 p.$d23 cm. 225 | $aMathematics and its applications$v2 410 0$1001MIL0073216$12001 $aMathematics and its applications$v2 606 $aAlgoritmi$2FIR$3CFIC033498$9E 606 $aElaboratori elettronici$xProgrammazione$2FIR$3CFIC000860$9E 676 $a005.1$9PROGRAMMAZIONE$v14 676 $a005.1$9PROGRAMMAZIONE$v22 700 1$aSellers$b, Peter H.$3MILV050265$4070$050498 801 3$aIT$bIT-000000$c20080213 850 $aIT-BN0095 $aIT-NA0212 901 $bNAP 01$cSALA DING $n$ 901 $bNAP IB$cMONOGRAFIE$n$ 912 $aMIL0073238 950 0$aBiblioteca Centralizzata di Ateneo$c1 v.$d 01SALA DING 005.1 SEL.co$e 0102 0000046555 VMA A4 1 v.$fY $h20030210$i20030210 977 $a 01$a IB 996 $aCombinatorial Complexes$9340443 997 $aUNISANNIO