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This study establishes a rigorous proof of random-matrix spectral ramps in static, geometrically local Hamiltonians, extending previous findings from periodically driven Floquet systems to time-independent settings. By embedding dual-unitary circuit spectra into local many-body systems, the authors provide a new diagnostic for quantum chaos that applies without requiring external driving protocols. This advancement deepens the theoretical understanding of how universal statistical signatures emerge in fundamental, undriven quantum matter.
Provable random-matrix spectral ramp in a static, geometrically local Hamiltonian
arXiv:2606.30635v2 Announce Type: replace Abstract: Quantum chaos is commonly associated with the emergence of random-matrix statistics in the spectra of quantum systems. A useful diagnostic is provided by the spectral form factor (SFF), which for random matrix ensembles displays a universal linear-growth regime (`ramp'). In the last decade, a landmark result by Bertini, Kos and Prosen (BKP) identified for the first time a class of geometrically local quantum dynamics of finite-dimensional particles where the SFF provably exhibits a random-matrix ramp: periodically driven (Floquet) qudit chains whose evolution is described by `dual-unitary' circuits. Here, building on the BKP result and on a recently proposed variant of the Feynman-Kitaev clock construction, we obtain a spectral ramp in a class of static, geometrically local Hamiltonians. Our strategy is to embed the Floquet quasienergy spectrum of a dual-unitary circuit into the energy spectrum of a static local Hamiltonian, and to prove that the latter's connected SFF inherits the BKP ramp within a symmetry sector. This is to our knowledge the first proof of a spectral ramp in a time-independent, geometrically local many-body system with finite local Hilbert space dimension.
Abstract:Quantum chaos is commonly associated with the emergence of random-matrix statistics in the spectra of quantum systems. A useful diagnostic is provided by the spectral form factor (SFF), which for random matrix ensembles displays a universal linear-growth regime (`ramp'). In the last decade, a landmark result by Bertini, Kos and Prosen (BKP) identified for the first time a class of geometrically local quantum dynamics of finite-dimensional particles where the SFF provably exhibits a random-matrix ramp: periodically driven (Floquet) qudit chains whose evolution is described by `dual-unitary' circuits. Here, building on the BKP result and on a recently proposed variant of the Feynman-Kitaev clock construction, we obtain a spectral ramp in a class of static, geometrically local Hamiltonians. Our strategy is to embed the Floquet quasienergy spectrum of a dual-unitary circuit into the energy spectrum of a static local Hamiltonian, and to prove that the latter's connected SFF inherits the BKP ramp within a symmetry sector. This is to our knowledge the first proof of a spectral ramp in a time-independent, geometrically local many-body system with finite local Hilbert space dimension.
4 + 2 + 2 pages, 3 figures. v2: added references, fixed typos
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th)
arXiv:2606.30635 [quant-ph]
(or arXiv:2606.30635v2 [quant-ph] for this version)
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