Quantum Ising chains with boundary fields

We present a detailed study of the finite one-dimensional quantum Ising chain in a transverse field in the presence of boundary magnetic fields coupled with the order-parameter spin operator. We consider two magnetic fields located at the boundaries of the chain that have the same strength and that are aligned in the same or in the opposite direction. We derive analytic expressions for the gap in all phases for large values of the chain length L, as a function of the boundary field strength. We also investigate the behaviour of the chain in the quantum ferromagnetic phase for oppositely aligned fields, focusing on the magnet-to-kink transition that occurs at a finite value of the magnetic field strength. At this transition we compute analytically the finite-size crossover functions for the gap, the magnetisation profile, the two-point correlation function, and the density of fermionic modes. As the magnet-to-kink transition is equivalent to the wetting transition in two-dimensional classical Ising models, our results provide new analytic predictions for the finite-size behaviour of Ising systems in a strip geometry at this transition.