Phase Transition in the Density of States of Quantum Spin Glasses

Erdős, László; Schröder, Dominik

doi:10.1007/s11040-014-9164-3

Cited by 86 publications

(150 citation statements)

References 5 publications

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“…In this work, our goal is to provide a full all-energy solution to the model in a slightly different scaling, which is the double-scaled SYK [19,30]. In this limit, p is not held fixed (as N → ∞) but rather is proportional to √ N (and is always assumed to be even), i.e.,…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…However, it is enough for us to take them to be independent random variables, with zero mean and uniformly bounded moments independent of N [30]. 1 They even need not be identically distributed, as in this limit only their standard deviation matters.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…It is clear that if p is small enough (for example, fixed), then with probability approaching 1, as N → ∞, there will not be a chance that two randomly chosen sets of size p will intersect. In our case, with p scaling according to (1.2), as shown in Appendix A (following [30]) the number of sites in the intersection I j ∩ I j is Poisson distributed with mean p 2 /N . Furthermore, different intersections are distinct with probability approaching 1 (for example, 3 different After commuting the terms, the pairs are neighboring, each giving just a sign, such that all of these signs together cancel the i kp/2 .…”

Section: Chord Diagramsmentioning

confidence: 99%

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Towards a full solution of the large N double-scaled SYK model

Berkooz

Isachenkov

Narovlansky

et al. 2019

J. High Energ. Phys.

119

228

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We compute the exact, all energy scale, 4-point function of the large N doublescaled SYK model, by using only combinatorial tools and relating the correlation functions to sums over chord diagrams. We apply the result to obtain corrections to the maximal Lyapunov exponent at low temperatures. We present the rules for the non-perturbative diagrammatic description of correlation functions of the entire model. The latter indicate that the model can be solved by a reduction of a quantum deformation of SL(2), that generalizes the Schwarzian to the complete range of energies.

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Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Section: Chord Diagramsmentioning

confidence: 99%

See 1 more Smart Citation

Towards a full solution of the large N double-scaled SYK model

Berkooz

Isachenkov

Narovlansky

et al. 2019

J. High Energ. Phys.

119

228

View full text Add to dashboard Cite

show abstract

“…Moreover, we have derived a compact analytical expression based on the known [64,65] spectral density for Q-Hermite polynomials. We leave the details of the calculation to the Appendix B and state here the final result [64]:…”

Section: The Resolventmentioning

confidence: 99%

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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“…The thermodynamic quantities can be calculated using (20) and (21): The relation between g m and β is given by (13) as…”

Section: Scaling Modelmentioning

confidence: 99%

Thermodynamics and many body chaos for generalized large q SYK models

Jiang

Yang

2019

J. High Energ. Phys.

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This paper considers a type of generalized large q SYK models which include multibody interactions between Majorana fermions. We derive an effective action in the limit of large N and large q (with q 2 N small), and find a universal expression for thermodynamical quantities. We also consider the chaos exponent using the retarded kernel method and find an efficient way to calculate the Lyapunov exponent for generalized large q SYK models numerically.

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Phase Transition in the Density of States of Quantum Spin Glasses

Cited by 86 publications

References 5 publications

Towards a full solution of the large N double-scaled SYK model

Towards a full solution of the large N double-scaled SYK model

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

Thermodynamics and many body chaos for generalized large q SYK models

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