QUANTUM TRANSVERSE FIELD ISING MODEL

Quantum phase transition at Γ/J = 1

|m| = ? | ⟨σx⟩ = ?
0.50
12
0.20 J
The 1D Transverse Field Ising Model: H = −J Σ σᵢᶻσᵢ₊₁ᶻ − Γ Σ σᵢˣ. This is exactly solvable via Jordan-Wigner fermions. It has a quantum phase transition at Γ/J = 1: for Γ < J the ground state is ferromagnetically ordered (⟨σᶻ⟩ ≠ 0); for Γ > J quantum fluctuations destroy order. The critical point is a quantum critical point with dynamical exponent z=1 and ν=1. Visualization shows spin configurations drawn from the thermal density matrix at temperature T.