Long distance entanglement in one-dimensional quantum systems under sinusoidal deformation

We investigate entanglement generation in one-dimensional quantum spin systems with the sinusoidal deformation. In the system, the energy scale of each local term in the Hamiltonian is modified according to a position-dependent function \sin^\alpha[\frac{\pi}{N} (x - \frac{1}{2})], where x is the position of the local term and N is the length of the system. We show that at zero temperature the system with \alpha \ge 2 is able to generate a sizable entanglement between two spins at open edges even when the two spins are infinitely far apart. This long-distance entanglement is rather robust against thermal fluctuations and survives up to a temperature that decays with the system size slowly, in an algebraic form.