Dynamic crystallization in a quantum Ising chain

The topological degeneracy of ground states in transverse field Ising chain cannot be removed by local perturbation and allows it to be a promising candidate for topological computation. We study the dynamic processes of crystallization and dissolution for the gapped ground states in an Ising chain. For this purpose, the real-space renormalization method is employed to build an effective Hamiltonian that captures the low-energy physics of a given system. We show that the ground state and the first-excited state of an $\left( N+1\right)$-site chain can be generated from that of the $N$-site one by adding a spin adiabatically and vice versa. Numerical simulation shows that the robust quasidegenerate ground states of finite-size chain can be prepared with high fidelity from a set of noninteracting spins by a quasiadiabatic process. As an application, we propose a scheme for entanglement transfer between a pair of spins and two separable Ising chains as macroscopic topological qubits.