Publisher’s Note: Supersymmetric Sachdev-Ye-Kitaev models [Phys. Rev. D 
<b>95</b>
, 026009 (2017)]

Fu, Wenbo; Gaiotto, Davide; Maldacena, Juan; Sachdev, Subir

doi:10.1103/physrevd.95.069904

Cited by 62 publications

(82 citation statements)

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“…This result agrees up to order 1=q 2 with the exact result [52] of s 0 obtained by using path integral techniques. We note that s 0 is larger than the value of s 0 in the even q case, where the nontrivial contribution to the entropy is π 2 =4q 2 .…”

Section: Thermodynamic Propertiessupporting

confidence: 80%

“…If we identify −E 2 0 log jηj ¼ J this is exactly the saddle point equation obtained in [52]. Taking the large N limit, it gives the free energy obtained in [52],…”

Section: Thermodynamic Propertiesmentioning

confidence: 99%

“…Unless specified otherwise J ≡ 1. This Hamiltonian is supersymmetric with global symmetries that, depending on N, correspond to one of the chiral and superconducting random matrix ensembles [52,56]. In this paper we will study the thermodynamical properties of the Hamiltonian, but we will analyze the spectral properties of the supercharge for E ∼ 0 corresponding to the ground state and low energy excitations of the Hamiltonian.…”

Section: Model Average Spectral Density and Thermodynamic Propermentioning

confidence: 99%

“…Depending on N, the supersymmetric SYK model [52,55] has additional chiral and discrete symmetries. The analysis of thermodynamic properties has revealed that the main differences with respect to the original SYK model are in the region close to the ground state E ≈ 0.…”

Section: Universal Microscopic Spectral Densitymentioning

confidence: 99%

“…Recently, different extensions of the SYK model have been studied including several fermionic flavors [42,43], higher dimensions [44][45][46][47][48], one plus two-body interactions [49][50][51], with supersymmetry [52][53][54][55][56][57][58][59] and with no disorder [37,60,61].…”

Section: Introductionmentioning

confidence: 99%

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Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

2018

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We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 þ 1 dimensions. We have found that, close to the ground state E ≈ 0, discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N, which we compute analytically and numerically, grows exponentially with N for E ≈ 0. However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈ 0, the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first OðNÞ eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈ 0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N. Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor gðtÞ, obtained from the connected twolevel correlation function of the unfolded spectrum, decays as 1=t 2 for times shorter but comparable to the Thouless time with gð0Þ related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

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Section: Thermodynamic Propertiessupporting

confidence: 80%

“…If we identify −E 2 0 log jηj ¼ J this is exactly the saddle point equation obtained in [52]. Taking the large N limit, it gives the free energy obtained in [52],…”

Section: Thermodynamic Propertiesmentioning

confidence: 99%

Section: Model Average Spectral Density and Thermodynamic Propermentioning

confidence: 99%

Section: Universal Microscopic Spectral Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

2018

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Diffusion in higher dimensional SYK model with complex fermions

Cai

Gao

2018

J. High Energ. Phys.

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We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential µ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.

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Warped Schwarzian theory

Afshar

2020

J. High Energ. Phys.

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We consider the (twisted) warped Virasoro group Diff(S 1 )⋉ C ∞ (S 1 ) in the presence of its three cocycles. We compute the Kirillov-Kostant-Souriau symplectic 2-form on coadjoint orbits. We then construct the Euclidean action of the 'warped Schwarzian theory' associated to the orbit with SL(2,R)×U(1) stabilizer as the effective theory of the reparametrization over the base circle and evaluate the corresponding one-loop-exact path integral.

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Publisher’s Note: Supersymmetric Sachdev-Ye-Kitaev models [Phys. Rev. D 95 , 026009 (2017)]

Cited by 62 publications

References 0 publications

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

Diffusion in higher dimensional SYK model with complex fermions

Warped Schwarzian theory

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