Order-disorder transition in a fully frustrated transverse-field Ising chain

An antiferromagnetic Ising model on the Delta chain, with a macroscopic ground state degeneracy and exponentially decaying spin correlation functions, is studied. By introducing transverse magnetic fields Gamma on spins at tips of the triangles and lambdaGamma on spins on the bottom chain, we study the ground state as a function of lambda and Gamma. The lambda = 0 problem is exactly solved and the ground state has a staggered magnetization on the bottom chain for any Gamma > 0. Because the transverse field on the bottom chain with finite A destroys the staggered order, the order disorder transition occurs as lambda is increased. We calculate the transition point lambda(c)(Gamma/J) as a function of Gamma/J, where J denotes the magnitude of the exchange interaction, by using the series expansion method around the lambda = 0 limit and conclude that lambda(c)(Gamma/J = +0) similar or equal to 0.9459. It is shown that states in the degenerate ground state manifold at Gamma = 0 are crucial in getting a finite value of lambda(c)(+0).