Quantum Critical Point: Transverse-Field Ising Model
Ground-state phase transition driven by quantum fluctuations
The 1D transverse-field Ising model H = −J Σσᵢᶻσᵢ₊₁ᶻ − Γ Σσᵢˣ has an exact quantum phase transition at Γ/J = 1. For Γ < J the ground state is ferromagnetically ordered; for Γ > J quantum fluctuations destroy order. At criticality the gap closes, correlation length diverges, and the system is described by a c=1/2 conformal field theory.