Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

We investigate the effects of smooth inhomogeneities at first-order quantum transitions (FOQT), such as those arising from the presence of a space-dependent external field, which smooths out the typical discontinuities of the low-energy properties. We argue that scaling phenomena develop at the transition region where the external field takes the value corresponding to the FOQT of the homogenous system. We present numerical evidence of such scaling phenomena at the FOQTs of quantum Ising chains, driven by a parallel magnetic field when the system is in the ferromagnetic phase, and at the FOQT of the q-state Potts chain for q>4, driven by an even temperature-like parameter giving rise to a discontinuity of the ground-state energy density.