Finite-size scaling at first-order quantum transitions

TL;DR

This paper investigates finite-size effects at first-order quantum transitions, revealing a universal finite-size scaling behavior governed by the ratio of perturbation energy to the finite-size energy gap, with broad applicability.

Contribution

It introduces a finite-size scaling framework for FOQTs based on the energy gap and boundary conditions, supported by analytical and numerical results.

Findings

Finite-size scaling behavior is governed by the ratio of perturbation energy to the finite-size gap.

Boundary conditions significantly influence the size dependence of the energy gap.

Numerical results for the quantum Ising chain support the proposed FSS framework.

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 ansatzes.