Quantum Critical Point — Transverse-Field Ising

The 1D transverse-field Ising model hosts a quantum phase transition at h/J = 1, driven by quantum fluctuations at T = 0.

h/J (field/coupling): Temperature:

h/J = 1.00 | ⟨σˣ⟩ = 0.00 | ⟨mz⟩ = 0.00 | Phase: critical

H = −J Σ σⁱzσʲz − h Σ σⁱx. At h/J < 1: ferromagnet (⟨σz⟩≠0). At h/J > 1: quantum paramagnet (⟨σx⟩≠0). QCP at h/J = 1: diverging correlation length, gap ∝ |h−J|, universality class = 2D classical Ising (z=1).