Quantum phase transitions in the transverse one-dimensional Ising model with four-spin interactions

Abstract

In this work we investigate the quantum phase transitions at zero temperature of the one-dimensional transverse Ising model with an extra term containing four-spin interactions. The competition between the energy couplings of the model leads to an interesting zero-temperature phase diagram. We use a modified Lanczos method to determine the ground state and the first excited state energies of the system, with sizes of up to 20 spins. We apply finite size scaling to the energy gap to obtain the boundary region where ferromagnetic to paramagnetic transition takes place. We also find the critical exponent associated with the correlation length. We find a degenerate $⟨3,1⟩$ phase region. The first-order transition boundary between this phase and the paramagnetic phase is determined by analyzing the behavior of the transverse spin susceptibility as the system moves from one region to the other.