Quantum phase transition in the transverse field Ising model on a Δ chain

We study quantum phase transition in the fully frustrated Δ chain Ising model under transverse fields Γ at spins on tops of the triangles and λΓ at ones on bottoms of the triangles, by using perturbation expansions, the numerical diagonalization method and a mean-field approximation with the Jordan-Wigner transformation. The system with λ=0 has a ground state with staggered order in the bottom chain for Γ>0. The transverse field at least as large as λcΓ destroys the staggered order. We calculate the critical point λc(Γ/J), where J denotes the antiferromagnetic exchange interaction, and obtain λc(Γ/J)≤λc(+0)=0.946