Integrable versus Chaotic Entanglement Dynamics

Integrable and chaotic dynamics provide different baselines for entanglement growth. Integrability preserves extensive quasiparticle data; chaotic dynamics can support coarse-grained membrane laws after local equilibration. Localized slow dynamics is a third comparator, not an extreme point on a one-parameter integrable-to-chaotic axis.

Required background. Entanglement growth supplies the direct curves being classified.

Helpful background. Quasiparticle growth supplies the integrable model, and membrane entanglement supplies the chaotic coarse-grained model.

Matched baselines

Compare three regulated local systems at matched energy density, local Hilbert-space truncation, interaction range, initial correlation length, and region geometry:

1. an integrable Hamiltonian with known quasiparticle dispersion;
2. a nonintegrable perturbation with level statistics and local relaxation consistent with chaos;
3. a disordered localized or long-prethermal comparator.

Measure $\Delta S_A(t)$ for several $A$, mutual information between separated regions, conserved densities, and finite-size saturation. Use independent diagnostics to establish the dynamical class; do not classify a model from the entropy curve that is then explained by that classification.

Expected distinctions

An integrable quench can show ballistic entropy growth quantitatively described by mode-dependent production entropies and dressed velocities, as tested by Alba and Calabrese 2017, Eqs. (1)–(4), pp. 7947–7949. A chaotic system can also show linear growth, but a state-dependent quasiparticle pair decomposition is generally not the robust explanation; Nahum et al. 2017, §§ II–IV instead derive hydrodynamic growth and fluctuations in a random-unitary model. A localized system can show slow, often logarithmic entanglement growth while transport remains strongly suppressed, as demonstrated for interacting disordered chains by Bardarson, Pollmann, and Moore 2012, Eqs. (1)–(3).

The leading form alone is not decisive. Fit the integrable quasiparticle formula using independently determined occupations, and fit the chaotic membrane tension on one geometry before predicting another. Compare residuals and out-of-sample predictions.

Integrable, chaotic, localized, and open evolution are alternative dynamical-class inputs. Each licenses different effective reductions between microscopic evolution and entropy data. The map is schematic.

Crossover tests

Add a weak integrability-breaking perturbation $gV$. For times shorter than a scattering scale, quasiparticle behavior may persist; for longer times, chaotic relaxation can emerge. Vary $g$ and seek a collapse in $t/t_{\rm cross}(g)$. Likewise, finite disordered systems can display long preasymptotic slow dynamics without establishing stable localization. Increase both time and size and inspect rare-region sensitivity.

Transferring a law between dynamical classes or fitting only before the crossover time can create a false asymptotic classification. Weak breaking and rare-region controls expose this failure. The map is schematic.

Evidence boundary

This comparison reflects results available through 10 August 2026. Quasiparticle and random-circuit/membrane baselines are quantitatively controlled in important model classes. The classification of a particular continuum QFT still requires its own scaling window, conserved quantities, and out-of-sample diagnostic tests.

References

• Alba, Vincenzo, and Pasquale Calabrese. “Entanglement and Thermodynamics after a Quantum Quench in Integrable Systems.” Proceedings of the National Academy of Sciences 114 (2017): 7947–7951. DOI.
• Bardarson, Jens H., Frank Pollmann, and Joel E. Moore. “Unbounded Growth of Entanglement in Models of Many-Body Localization.” Physical Review Letters 109 (2012): 017202. DOI.
• Nahum, Adam, Jonathan Ruhman, Sagar Vijay, and Jeongwan Haah. “Quantum Entanglement Growth under Random Unitary Dynamics.” Physical Review X 7 (2017): 031016. DOI.