title: Finite-size scaling at first-order quantum transitions.
abstract: We study finite-size effects at first-order quantum transitions (FOQTs). We show that the low-energy properties show a finite-size scaling (FSS) behavior, the relevant scaling variable being the ratio of the energy associated with the perturbation driving the transition and the finite-size energy gap at the FOQT point. The size dependence of the scaling variable is therefore essentially determined by the size dependence of the gap at the transition, which in turn depends on the boundary conditions. Our results have broad validity and, in particular, apply to any FOQT characterized by the degeneracy and crossing of the two lowest-energy states in the infinite-volume limit. In this case, a phenomenological two-level theory provides exact expressions for the scaling functions. Numerical results for the quantum Ising chain in transverse and parallel magnetic fields support the FSS Ansätzes.
authors.affiliation: Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy.
authors.forename: Massimo
authors.initials: M
authors.lastname: Campostrini
authors.affiliation: Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy.
authors.forename: Jacopo
authors.initials: J
authors.lastname: Nespolo
authors.affiliation: Dipartimento di Fisica di "Sapienza," Università di Roma and INFN, Sezione di Roma I, I-00185 Roma, Italy.
authors.forename: Andrea
authors.initials: A
authors.lastname: Pelissetto
authors.affiliation: Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy.
authors.forename: Ettore
authors.initials: E
authors.lastname: Vicari