20.500.12556/RUL-181122 Full eigenstate thermalization via free cumulants in quantum lattice systems The eigenstate thermalization hypothesis (ETH) has been established as the general framework to understand quantum statistical mechanics. Only recently has the attention been paid to so-called full ETH, which accounts for higher-order correlations among matrix elements, and that can be rationalized theoretically using the language of free probability. In this work, we perform the first numerical investigation of the full ETH in physical many-body systems with local interactions by testing the decomposition of higher-order correlators into thermal free cumulants for local operators. We perform exact diagonalization on two classes of local nonintegrable (chaotic) quantum many-body systems: spin chain Hamiltonians and Floquet brickwork unitary circuits. We show that the dynamics of four-time correlation functions are encoded in fourth-order free cumulants, as predicted by ETH. Their dependence on frequency encodes the physical properties of local many-body systems and distinguishes them from structureless, rotationally invariant ensembles of random matrices. eigenstate thermalization quantum chaos quantum circuits quantum statistical mechanics quantum spin chains Floquet systems random matrix theory termalizacija lastnih stanj kvantni kaos kvantna vezja kvantna statistična mehanika kvantna spinske verige Floquetovi sistemi teorija naključnih matrik true false true Angleški jezik Slovenski jezik Članek v reviji 2026-03-25 15:58:24 2026-03-25 15:58:26 2026-04-13 08:17:44 0000-00-00 00:00:00 2025 0 0 Str. 140404-1-140404-7 iss. 14 Vol. 134 2025 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 536.93 0031-9007 10.1103/PhysRevLett.134.140404 273055747 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.140404 1 f44069db-285a-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=231309 2303.00713v4.pdf 2303.00713v4.pdf 1 E3479FAD468E51089BC275BA48743ED9 067ca8c50305bd660e79adc30c23d064deb50b11498606e73de23a63c3965c0a 793ecd97-285b-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=231310 Fakulteta za matematiko in fiziko 0 0 0