Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes

[2502.04152] Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes Skip to main content Search Submit Donate Log in Condensed Matter > Statistical Mechanics arXiv:2502.04152 (cond-mat) [Submitted on 6 Feb 2025] Title: Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes Authors: Vijay Kumar , Tomaž Prosen , Dibyendu Roy View PDF HTML (experimental) Abstract: We show the emergence of random matrix theory (RMT) spectral correlations in the chaotic phase of generic periodically kicked interacting quantum many-body systems by analytically calculating spectral form factor (SFF), $K(t)$, up to two leading orders in time, $t$. We explicitly consider the presence or absence of time reversal ($\mathcal{T}$) symmetry to investigate all three Dyson's symmetry classes. Our derivation only assumes random phase approximation to enable ensemble average. For $\mathcal{T}$-invariant systems with $\mathcal{T}^2=1$, we show that beyond the Thouless time $t^*$, the SFF takes the form $K(t)\simeq 2t-2t^2/\mathcal{N}$ up to second order in time, where $\mathcal{N}$ is the Hilbert space dimension. This is identical to the result from circular orthogonal ensemble of RMT. In the absence of $\mathcal{T}$-symmetry, we show that $K(t)\simeq t$ beyond $t^*$, and there is no universal term in the second order, unlike the $\mathcal{T}^2=1$ case, in agreement with the result of circular unitary ensemble. For $\mathcal{T}$-invariant systems with $\mathcal{T}^2=-1$, we show that $K(t)\simeq 2t+2t^2/\mathcal{N}$ up to two orders in time beyond $t^*$, in agreement with the result of circular symplectic ensemble. In all three cases, the system-size, $L$, scaling of $t^*$ is determined by eigenvalues of a doubly stochastic matrix $\mathcal{M}$. For strongly interacting fermionic chains, $\mathcal{M}$ is $SU(2)$ invariant in all three cases, leading to $t^*\propto L^2$ in the presence of $U(1)$ symmetry. In the absence of $U(1)$ symmetry, we find $t^*\propto L^0$, due to gapped non-degenerate second-largest eigenvalue of $\mathcal{M}$ or $t^*\propto \ln(L)$ due to gapped second-largest eigenvalue with degeneracy $\propto L^\zeta$. Our calculation of SFF is plausible in higher space dimensions as well, where similar system-size scalings of $t^*$ can be obtained. Subjects: Statistical Mechanics (cond-mat.stat-mech) ; Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD); Quantum Physics (quant-ph) Cite as: arXiv:2502.04152 [cond-mat.stat-mech] (or arXiv:2502.04152v1 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2502.04152 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. X 16, 031019 (2026) Related DOI : https://doi.org/10.1103/kwh6-hncn Focus to learn more DOI(s) linking to related resources Submission history From: Vijay Kumar [ view email ] [v1] Thu, 6 Feb 2025 15:37:18 UTC (1,182 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2025-02 Change to browse by: cond-mat math math-ph math.MP nlin nlin.CD quant-ph References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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