Bethe Ansatz (1931):
E(k) = J(1−cos k)
E_k = —
k_magnon = —π/N
v_group = —
Magnon #: 0
GS energy: —
E(k) = J(1−cos k)
E_k = —
k_magnon = —π/N
v_group = —
Magnon #: 0
GS energy: —
The 1D Heisenberg XXZ model H=J Σ(SᵢSᵢ₊₁+Δ Sᵢ_z Sᵢ₊₁_z) is exactly solvable via Bethe Ansatz (1931). Excitations are magnons (spin waves): flipped spin propagates as a quasiparticle with E(k)=J(1−cos k), gap Δ-dependent. Δ=0 → XX model, Δ=1 → Heisenberg, Δ>1 → Ising-like.