Analytical spectral density of the Sachdev-Ye-Kitaev model at finite 
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Garcı́a-Garcı́a, Antonio M.; Verbaarschot, J. J. M.

doi:10.1103/physrevd.96.066012

Phys. Rev. D

2017

DOI: 10.1103/physrevd.96.066012

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Analytical spectral density of the Sachdev-Ye-Kitaev model at finite N

Antonio M. Garcı́a-Garcı́a

¹

,

J. J. M. Verbaarschot

²

Abstract: We derive an approximate analytical formula for the spectral density of the q-body This spectral density reproduces the known result for the free energy in the large q and N limit at arbitrary values of the temperature. In the infrared region, where the SachdevYe-Kitaev model is believed to have a gravity-dual, the analytical spectral density is given. It therefore has a square-root edge, as in random matrix ensembles, followed by an exponential growth, a distinctive feature of black holes and also of low ener… Show more

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Cited by 190 publications

(201 citation statements)

References 60 publications

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“…The symmetry classification of the N = 0 SYK model was given for a Hamiltonian with the most generic q-body interaction. The result, summarized in tables 2 and 3, includes the RMT classes C and D that did not show up in the preceding classification of [66][67][68][69]72]. Our results were corroborated by detailed numerics (figure 1).…”

Section: Discussionsupporting

confidence: 80%

Complete random matrix classification of SYK models with N $$ \mathcal{N} $$ = 0, 1 and 2 supersymmetry

Kanazawa¹,

Wettig

²

2017

J. High Energ. Phys.

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

show abstract

“…The symmetry classification of the N = 0 SYK model was given for a Hamiltonian with the most generic q-body interaction. The result, summarized in tables 2 and 3, includes the RMT classes C and D that did not show up in the preceding classification of [66][67][68][69]72]. Our results were corroborated by detailed numerics (figure 1).…”

Section: Discussionsupporting

confidence: 80%

Complete random matrix classification of SYK models with N $$ \mathcal{N} $$ = 0, 1 and 2 supersymmetry

Kanazawa¹,

Wettig

²

2017

J. High Energ. Phys.

Get access via publisher Add to dashboard Cite

Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…Therefore, this study has the potential to provide valuable insights into these areas of research. Finally, it is worth noting that while our results lie within the (3) limit, they also show a significant agreement with fixed finite p cases (as observed in a comparable situation by [33,36]). Section 6 will present a comparison of our analytical results with the numerical computation of the p = 4 case.…”

Section: Introductionsupporting

confidence: 87%

Non-commutative probability insights into the double-scaling limit SYK model with constant perturbations: moments, cumulants and q-independence

Wu¹

2024

J. Phys. A: Math. Theor.

0

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…This prevents us from obtaining a meaningful correction to the free energy by integrating δρ. This is indeed consistent with the fact that the SYK partition function is 1/N exact in the low temperature limit [3,29,30,43] where it is dominated by the spectral density for E ≈ E 0 , so 1/N 2 corrections in this region must be spurious.…”

Section: Spectral Density For Even Qsupporting

confidence: 82%

Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N2

García-García,

Jia,

Verbaarschot

2018

J. High Energ. Phys.

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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