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

Abstract 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 λ c Γ destroys the staggered order. We calculate the critical point λ c ( Γ / J ), where J denotes the antiferromagnetic exchange interaction, and obtain λ c ( Γ / J )⩽ λ c (+0)=0.946.