Sachdev-Ye-Kitaev Model — Non-Fermi Liquid Spectral Function

Conformal Green's function · |ω|^(−1/2) spectral density · T-dependence
A(ω) SYK spectral function
Fermi liquid A_FL(ω)
Im Σ(ω) self-energy
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The SYK model: N Majorana fermions with all-to-all random q-body interactions of variance J². In the large-N, low-T conformal limit: G(τ) ∝ (1/πT)^(2Δ) |sin(πTτ)|^(−2Δ) with Δ=1/q. Spectral function A(ω) = −(1/π)Im G^R(ω) shows a broad non-Fermi-liquid lineshape with |ω|^(2Δ−1) tails. Self-energy Im Σ ∝ |ω|^(1−2/q) — linear in ω for q→∞ (Fermi liquid), but non-analytic for finite q.