Finite-size scaling at the first-order quantum transitions of quantum Potts chains

We investigate finite-size effects at first-order quantum transitions. For this purpose we consider the one-dimensional q-state quantum Potts chain, in particular with q = 10, which undergoes a first-order transition, separating the quantum disordered and ordered phases with a discontinuity in the energy density of the ground state. In agreement with the general theory, around the transition the low-energy properties show finite-size scaling with respect to appropriate scaling variables. Their size dependence is particularly sensitive to boundary conditions, which is a specific feature of first-order quantum transitions. Finally, we also discuss the finite-size behavior of the q-state Potts model (q greater than or similar to 2) at the first-order transitions driven by a parallel magnetic field, occurring in the ferromagnetic phase.