Numerical estimate of the phase diagram of finite ANNNI chains in transverse field

We have estimated numerically the phase diagram of a one dimensional spin ½ quantum Ising model with competing nearest and next nearest neighbour interactions in presence of a transverse field. The method essentially is to diagonalise exactly the Hamiltonian for finite (≤10 spins) open chains and calculate the spin-spin correlations from the ground state eigenvector. The results obtained confirm the transition between ferromagnetic and paramagnetic phases for ℜ<0.5 and="" between="" antiphase="" and="" paramagnetic="" phase="" for="">ℜ>0.5. ( is the ratio of next nearest and nearest neighbour interactions.) The results perhaps indicate furthermore that (i) there is a disorder line passing through ℜ=0.5; (ii) the zero point quantum fluctuations destroy the order near ℜ=0.5 as the transverse field is switched on; and (iii) there is probably also a floating phase with slowly decayling correlation near the order-disorder phase boundary for ℜ>0.5