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arXiv:2607.03294

Many-body quantum chaos in excitonic spectra from first principles

Daniel Hernangómez‐Pérez, Rafael A. Molina

Published Jul 3, 2026• 0 citations
arXivHTMLPDF

Abstract

We demonstrate that realistic excitonic many-body Hamiltonians obtained from first-principles GW-Bethe-Salpeter equation calculations can exhibit quantum chaos governed by random-matrix universality. Considering a prototypical van der Waals heterostructure (WS$_2$-graphene), with and without lattice disorder, we analyze their energy-resolved spectral correlations and identify a disorder-driven crossover from regular to complete chaotic dynamics. We show that while pristine samples exhibit incomplete chaos (non-ergodicity) due to an approximate valley symmetry that restricts excitonic mixing, the presence of disorder-induced electronic flat bands act as a catalyst for valley mixing to drive the system into a fully developed chaotic (ergodic) regime with reduced symmetry. Crucially, fluctuations in many-body oscillator strengths are shown to follow universal Porter-Thomas statistics, directly linking the underlying quantum chaos and experimentally accessible optical observables. Finally, by examining long-range spectral correlations, we estimate the Thouless time associated to excitonic mixing across the entire many-body bandwidth. Our results establish excitons as a highly tunable platform for probing many-body ergodicity and its spectroscopic signatures in realistic interacting 2D materials.

DOI
10.48550/arxiv.2607.03294

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We demonstrate that realistic excitonic many-body Hamiltonians obtained from first-principles GW-Bethe-Salpeter equation calculations can exhibit quantum chaos governed by random-matrix universality. Considering a prototypical van der Waals heterostructure (WS2_22​-graphene), with and without lattice disorder, we analyze their energy-resolved spectral correlations and identify a disorder-driven crossover from regular to complete chaotic dynamics. We show that while pristine samples exhibit incomplete chaos (non-ergodicity) due to an approximate valley symmetry that restricts excitonic mixing, the presence of disorder-induced electronic flat bands act as a catalyst for valley mixing to drive the system into a fully developed chaotic (ergodic) regime with reduced symmetry. Crucially, fluctuations in many-body oscillator strengths are shown to follow universal Porter-Thomas statistics, directly linking the underlying quantum chaos and experimentally accessible optical observables. Finally, by examining long-range spectral correlations, we estimate the Thouless time associated to excitonic mixing across the entire many-body bandwidth. Our results establish excitons as a highly tunable platform for probing many-body ergodicity and its spectroscopic signatures in realistic interacting 2D materials.
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A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT).Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges.For single particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc.R. Soc.London, A400, 229 (1985)] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K(t) (Fourier transform of spectral pair correlation function), from semiclassics has been completed by Müller et al. [Phys.Rev. Lett.93, 014103 (2004)].In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming at the forefront even for simple many-body quantum systems, such as locally interacting spin chains.Such systems display two universal types of behaviour which are termed as the 'many-body localized phase' and 'ergodic phase'.In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder.Here we provide a clear theoretical explanation for these observations.We compute K(t) in the leading two orders in t and show its agreement with RMT for non-integrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin 1/2 models in a periodically kicking transverse field.In particular, we relate K(t) to partition functions of a class of twisted classical Ising models on a ring of size t, hence the leading order RMT behavior K(t)2t is a consequence of translation and reflection symmetry of the Ising partition function.
This work investigates the emergent thermalization regimes in a chaotic Tavis-Cummings (TC) model and their implications in quantum spectroscopy. While the TC model is a cornerstone of cavity quantum electrodynamics, traditional treatments often overlook many-body effects that arise in the thermodynamic limit. We utilize the Eigenstate Thermalization Hypothesis to demonstrate that a non-integrable excitonic Hamiltonian within the material manifold drives local thermalization. By tuning the polariton splitting ggg, we observe two dynamical regimes: a thermalizing regime at low interactions driven by quantum chaos and ergodicity, and a non-thermalizing regime at high interactions where strong coupling suppresses ergodicity. We further show that these regimes have direct implications on output photon statistics, specifically influencing the correlation times τcτ_cτc​ of the cavity population and the second-order correlation function g(2)(t+τ)g^{(2)}(t+τ)g(2)(t+τ). We propose that entangled-biphoton spectroscopy serves as an ideal experimental platform to probe these effects and to allow the characterization of the underlying many-body exciton-coupling disorder σσσ through coincidence measurements of the output. Taken together, these results exploit a naturally occurring many-body phenomenon to bridge theoretical predictions with experimental observables.
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