In this paper, we study the ground state of a one-dimensional exactly solvable model with a spiral order. While the model's energy spectrum is the same as the one-dimensional transverse field Ising model, its ground state manifests a spiral order with various periods. The quantum phase transition from a spiral-order phase to a paramagnetic phase is investigated in the perspectives of quantum information science and mechanics. We show that the modes of the ground-state fidelity and its susceptibility can identify the change of periodicity around the critical point. We also study the spin torsion modulus which defines the coefficient of the potential energy stored under a small rotation. We find that at the critical point, it is a constant; while away from the critical point, the spin torsion modulus tends to zero.
Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field
