Codes for studying the SYK model.
MATLABcodes folder contains codes for constructing the SYK Hamiltonian and doing the exact diagonalization.
spectral-form-factor.nb:
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import data from exact diagonalization of SYK Hamiltonian (raw data generated from the ''MATLABcodes'' folder in this repository),
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calcualte average adjacent level spacing ratio,
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unfold the spectra (slow, use Julia codes)
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calculate and plot the unfolded and connected spectral form factor(slow, use Julia codes).
JuliaCodes folder: do all the spectral form factor computation in spectral-form-factor.nb (and more) but much faster.
SYKmoments.nb: calculates the single-trace moments (up to Tr H^8) and double-trace moments (up to TrH^6 TrH^6) of SYK. Algorithms follow arXiv:1801.02696 and arXiv:1912.11923
double-trace-chord-diagram-classification:
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find equivalent chord diagrams due to cyclic permutation and reflection of ordering of gamaa matrices inside the two traces,
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different classes chord diagrams can still have the same intersection structures after this classification, that I worked out by hands.