Quantum Critical Point
Hertz-Millis theory — non-Fermi liquid & quantum critical fan
Parameters
Tuning parameter r (distance to QCP):
0.00
Dynamical exponent z:
3
Correlation length exponent ν:
0.50
Disorder δ:
0.00
Hertz-Millis:
Action: S = Σ_q r|φ|² + q²|φ|²
+ |ω_n|/|q|^(z-2) + u|φ|⁴
Near QCP (r→0):
ξ ~ |r|^(-ν)
τ_c ~ ξ^z ~ |r|^(-νz)
NFL in quantum critical fan:
C/T ~ -log(T) (z=3, AFM)
ρ ~ T^(1+2/z)