Universal Equilibration Dynamics Of The Sachdev-Ye-Kitaev Model

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Soumik Bandyopadhyay¹, Philipp Uhrich¹, Alessio Paviglianiti^1,2، اور فلپ ہاک¹

¹Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Via Sommarive 14, Trento, I-38123, Italy
²International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy

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خلاصہ

Equilibrium quantum many-body systems in the vicinity of phase transitions generically manifest universality. In contrast, limited knowledge has been gained on possible universal characteristics in the non-equilibrium evolution of systems in quantum critical phases. In this context, universality is generically attributed to the insensitivity of observables to the microscopic system parameters and initial conditions. Here, we present such a universal feature in the equilibration dynamics of the Sachdev-Ye-Kitaev (SYK) Hamiltonian – a paradigmatic system of disordered, all-to-all interacting fermions that has been designed as a phenomenological description of quantum critical regions. We drive the system far away from equilibrium by performing a global quench, and track how its ensemble average relaxes to a steady state. Employing state-of-the-art numerical simulations for the exact evolution, we reveal that the disorder-averaged evolution of few-body observables, including the quantum Fisher information and low-order moments of local operators, exhibit within numerical resolution a universal equilibration process. Under a straightforward rescaling, data that correspond to different initial states collapse onto a universal curve, which can be well approximated by a Gaussian throughout large parts of the evolution. To reveal the physics behind this process, we formulate a general theoretical framework based on the Novikov–Furutsu theorem. This framework extracts the disorder-averaged dynamics of a many-body system as an effective dissipative evolution, and can have applications beyond this work. The exact non-Markovian evolution of the SYK ensemble is very well captured by Bourret–Markov approximations, which contrary to common lore become justified thanks to the extreme chaoticity of the system, and universality is revealed in a spectral analysis of the corresponding Liouvillian.

Featured image: Universal super-exponential equilibration dynamics of the QFI, $F_{mathcal{Q}}$, under the complex SYK$_4$ Hamiltonian.
(a) Illustration of the quench protocol. Left: Initial states are chosen as ground states of the Fermi–Hubbard (FH) Hamiltonian for different values of $U/mathcal{J}$ (other generic initial states yield equivalent results). The black and gray circles respectively represent occupied and empty fermionic modes. Dashed lines illustrate hopping of fermions between nearest-neighbor sites. Right: The system is evolved under the SYK$_4$ Hamiltonian, where spinless fermions (black circles) can hop to any empty fermionic mode (light gray circles). The disordered interaction strengths $left{J_{i_{1}i_{2};j_{1}j_{2}}right}$ are randomly sampled from independent Gaussian distributions.
(b) QFI averaged over $400$ disorder realizations, $mathbb{E}left[F_{mathcal{Q}}right]$, computed with respect to the operator $hat{R}$ defined in Eq. (6). Initial states from darker to lighter shade of blue are for $U/mathcal{J} = 0, 2, 4, 6, 8$, and $10$. The system equilibrates fast to the expectation value of the Gibbs infinite temperature state (dotted black line).
(c) Universality in the dynamics is revealed by rescaling to $mathcal{G}left(mathbb{E}left[F_{mathcal{Q}}right]right)$, as given in Eq. (3). Very good agreement is found to a Gaussian fit, $mathrm{exp}left[-(Jt/tau)^2right]$, with a fast decay constant of $tau = 1.52$ (dashed red curve). Data for $Q=8$ fermions occupying $N = 16$ fermionic modes.

► BibTeX ڈیٹا

@article{Bandyopadhyay2023universal, doi = {10.22331/q-2023-05-24-1022}, url = {https://doi.org/10.22331/q-2023-05-24-1022}, title = {Universal equilibration dynamics of the {S}achdev-{Y}e-{K}itaev model}, author = {Bandyopadhyay, Soumik and Uhrich, Philipp and Paviglianiti, Alessio and Hauke, Philipp}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1022}, month = may, year = {2023}<br /> }

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کی طرف سے حوالہ دیا گیا

[1] Debanjan Chowdhury, Antoine Georges, Olivier Parcollet, and Subir Sachdev, “Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids”, جدید طبیعیات کے جائزے 94 3, 035004 (2022).

[2] Jan C. Louw and Stefan Kehrein, “Thermalization of many many-body interacting Sachdev-Ye-Kitaev models”, جسمانی جائزہ B 105 7, 075117 (2022).

[3] Ceren B. Dağ, Philipp Uhrich, Yidan Wang, Ian P. McCulloch, and Jad C. Halimeh, “Detecting quantum phase transitions in the quasi-stationary regime of Ising chains”, آر ایکس سی: 2110.02995, (2021).

[4] الیسیو پاویگلیانیٹی، سومک بندیوپادھیائے، فلپ یوہرچ، اور فلپ ہوک، "سچدیو-ی-کیتائیو ماڈل کے چارج محفوظ شعبوں میں اوسط برابر وقت کے مشاہدے کے لیے آپریٹر کی ترقی کی عدم موجودگی"، جرنل آف ہائی انرجی فزکس 2023 3, 126 (2023).

[5] Philipp Uhrich, Soumik Bandyopadhyay, Nick Sauerwein, Julian Sonner, Jean-Philippe Brantut, and Philipp Hauke, “A cavity quantum electrodynamics implementation of the Sachdev–Ye–Kitaev model”, آر ایکس سی: 2303.11343, (2023).

[6] Ceren B. Daǧ, Philipp Uhrich, Yidan Wang, Ian P. McCulloch, and Jad C. Halimeh, “Detecting quantum phase transitions in the quasistationary regime of Ising chains”, جسمانی جائزہ B 107 9, 094432 (2023).

مذکورہ بالا اقتباسات سے ہیں۔ SAO/NASA ADS (آخری بار کامیابی کے ساتھ 2023-05-25 00:04:19)۔ فہرست نامکمل ہو سکتی ہے کیونکہ تمام ناشرین مناسب اور مکمل حوالہ ڈیٹا فراہم نہیں کرتے ہیں۔

On Crossref کی طرف سے پیش خدمت کاموں کے حوالے سے کوئی ڈیٹا نہیں ملا (آخری کوشش 2023-05-25 00:04:17)۔

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ماخذ: https://quantum-journal.org/papers/q-2023-05-24-1022/

ٹائم اسٹیمپ: 24 فرمائے، 2023