Sachdev-Ye-Kitaev model: Non-self-averaging properties of the energy spectrum

• URL: http://arxiv.org/abs/2208.11008v1
• Date: Tue, 23 Aug 2022 14:42:44 GMT
• Title: Sachdev-Ye-Kitaev model: Non-self-averaging properties of the energy spectrum
• Authors: Richard Berkovits
• Abstract summary: The short time (large energy) behavior of the Sachdev-Ye-Kitaev model (SYK) is one of the main motivation to the growing interest garnered by this model. True chaotic behaviour sets in at the Thouless time, which can be extracted from the energy spectrum. It is shown that the SYK model in non-self-averaging even in the thermodynamic limit which must be taken into account.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The short time (large energy) behavior of the Sachdev-Ye-Kitaev model (SYK) is one of the main motivation to the growing interest garnered by this model. True chaotic behaviour sets in at the Thouless time, which can be extracted from the energy spectrum. In order to do so, it is necessary to unfold the spectrum, i.e., to filter out global tendencies. Using a simple ensemble average for unfolding results in a parametically low estimation of the Thouless energy. By examining the behavior of the spectrum as the distribution of the matrix elements is changed into a log-normal distribution it is shown that the sample to sample level spacing variance determines this estimation of the Thouless energy. Using the singular value decomposition method, SVD, which filters out these sample to sample fluctuations, the Thouless energy becomes parametrically much larger, essentially of order of the band width. It is shown that the SYK model in non-self-averaging even in the thermodynamic limit which must be taken into account in considering its short time properties.

Related papers

• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Quantum thermodynamics of the Caldeira-Leggett model with non-equilibrium Gaussian reservoirs [0.0]
  We introduce a non-equilibrium version of the Caldeira-Leggett model in which a quantum particle is strongly coupled to a set of engineered reservoirs. Strongly displaced/squeezed reservoirs can be used to generate an effective time dependence in the system Hamiltonian. We show the quantum-classical correspondence between the heat statistics in the non-equilibrium Caldeira-Leggett model and the statistics of a classical Langevin particle under the action of squeezed and displaced colored noises.
  arXiv  Detail & Related papers  (2024-04-30T21:41:34Z)
• Iterated Denoising Energy Matching for Sampling from Boltzmann Densities [109.23137009609519]
  Iterated Denoising Energy Matching (iDEM) iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our matching objective. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5times$ faster.
  arXiv  Detail & Related papers  (2024-02-09T01:11:23Z)
• Randomly Pruning the Sachdev-Ye-Kitaev model [0.0]
  The Sachdev-Ye-Kitaev model (SYK) is renowned for its short-time chaotic behavior. The Thouless energy, representing the energy scale at which the universal chaotic behavior in the energy spectrum ceases, can be determined from the spectrum itself.
  arXiv  Detail & Related papers  (2024-01-14T16:20:16Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• The open Haldane-Shastry chain: thermodynamics and criticality [0.0]
  We study the thermodynamics and criticality of the su($m|n$) Haldane-Shastry chain of $BC_N$ type. We identify the critical intervals in chemical potential space and compute their corresponding Fermi velocities.
  arXiv  Detail & Related papers  (2022-06-06T14:41:06Z)
• An Energy-Based Prior for Generative Saliency [62.79775297611203]
  We propose a novel generative saliency prediction framework that adopts an informative energy-based model as a prior distribution. With the generative saliency model, we can obtain a pixel-wise uncertainty map from an image, indicating model confidence in the saliency prediction. Experimental results show that our generative saliency model with an energy-based prior can achieve not only accurate saliency predictions but also reliable uncertainty maps consistent with human perception.
  arXiv  Detail & Related papers  (2022-04-19T10:51:00Z)
• Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs [0.0]
  We study the scaling of the Thouless time in the Anderson model on random regular graphs with on-site disorder. We find that the scaling of the Thouless time is consistent with the existence of a sub-diffusive regime anticipating the localized phase.
  arXiv  Detail & Related papers  (2022-01-12T19:56:56Z)
• Particle Dynamics for Learning EBMs [83.59335980576637]
  Energy-based modeling is a promising approach to unsupervised learning, which yields many downstream applications from a single model. The main difficulty in learning energy-based models with the "contrastive approaches" is the generation of samples from the current energy function at each iteration. This paper proposes an alternative approach to getting these samples and avoiding crude MCMC sampling from the current model.
  arXiv  Detail & Related papers  (2021-11-26T23:41:07Z)
• Distribution of Kinks in an Ising Ferromagnet After Annealing and the Generalized Kibble-Zurek Mechanism [0.8258451067861933]
  We consider a one-dimensional Isingmagnet induced by a temperature quench in finite time. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics. We consider linear, nonlinear, and exponential cooling schedules, among which the latter provides the most efficient shortcuts to cooling in a given time.
  arXiv  Detail & Related papers  (2021-05-19T13:58:33Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.