Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry-protected topological states

By Yi-Zhuang You, A. Ludwig, Cenke Xu. 2016

214 citations recorded by the source corpus.

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model for randomly interaction fermions in a quantum dot. This paper studies the properties of the many-body spectrum of the SYK model and finds a periodicity of the spectral properties in term of the number of fermion modes in the quantum dot. In particular, the level statistics of SYK spectrum are investigated. It is found that the many-body level spacing of the SYK model follows Wigner-Dyson statistics, consistent with the thermalizing nature of the SYK model. Interestingly, the level statistics goes through those of different random matrix ensembles periodically. The periodicity can be explained by viewing the SYK model as an effective model for the boundary of 1D interacting fermionic symmetry-protected topological states. The periodicity in the SYK spectrum is therefore tied to the classification of fermionic topological states in one dimension.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4f09efc51d5c052648d5a298b338437256968952

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Three dimensional view of the SYK/AdS duality (2017, unknown): “Interesting random matrix theory interpretations have been studied in [33{39].”
Quantum chaos and holographic tensor models (2016, methodology): “Furthermore, it was noted in [22, 23, 6] that the theory has a symmetry P that has been called a particle-hole symmetry11.”
A semiclassical ramp in SYK and in gravity (2018, methodology): “There are two important discrete symmetries to consider [63, 23, 64, 22, 65] • The fermion parity symmetry (−1) = (2i)N2 ψ1ψ2 .”
Quantum chaos and the complexity of spread of states (2022, unknown): “We have checked that the results in those cases are consistent with observations in the previous section about complexity and universality, and the results of [85].”
Black holes and random matrices (2016, methodology): “The theory also has a particle-hole symmetry under the operator [39, 32, 31]”
Supersymmetric SYK model and random matrix theory (2017, methodology): “This is accomplished by finding the symmetry of the theory (and has been already discussed in other works, see [54, 57]).”
Remarks on the Sachdev-Ye-Kitaev model (2016, result): “Further recent work in this or similar models includes [14, 15, 16, 17, 7, 18, 19].”
JT gravity and the ensembles of random matrix theory (2019, background): “First, although is not a random matrix theory in the sense we mean it in this paper, it is “close enough,” in that the correlations of nearby energy eigenvalues have a well-defined random matrix classification [65, 66, 67, 68].”
Numerical study of fermion and boson models with infinite-range random interactions (2016, methodology): “For NA < N/2, we find that SEE is proportional to NA, thus obeying the volume law, and so even the ground state obeys eigenstate thermalization [14].”
JT gravity as a matrix integral (2019, background): “One of the motivations for this work was to understand the origin of random matrix statistics in the SYK model [62, 63, 20, 13] from the gravitational perspective.”
Chaos, complexity, and random matrices (2017, methodology): “(2)For SYK with N Majoranas, particle-hole symmetry dictates the symmetry class of the spectrum, where N (mod 8) ≡ 2 or 6 corresponds to GUE statistics [23].”
Power-law out of time order correlation functions in the SYK model (2017, background): “However, statistical wave function/eigenvalue independence is a hallmark of random matrix models, and in view of the evidence for ergodic chaotic behavior shown by the SYK model at low energies [20, 13] may contain some truth.”