The spectral gap of the ferromagnetic XXZ chain

Tohru Koma, Bruno Nachtergaele

We prove that the spectral gap of the spin-1/2 ferromagnetic XXZ chain with Hamiltonian $H=-{\sum }_x{S}_x^{(1)}{S}_{x+1}^{(1)}+S_x^{(2)}{S}_{x+1}^{(2)}+\Delta S_x^{(3)}{S}_{x+1}^{(3)}$, is given…