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

TL;DR

This paper studies how smooth inhomogeneities affect first-order quantum transitions, revealing scaling phenomena at the transition region through numerical analysis of quantum Ising and Potts chains.

Contribution

It demonstrates the development of scaling phenomena at FOQTs due to inhomogeneous conditions, supported by numerical evidence in specific quantum spin chains.

Findings

Scaling phenomena occur at the transition region with inhomogeneities.

Numerical evidence from quantum Ising chains shows scaling behavior.

Similar phenomena observed in q-state Potts chains for q>4.

Abstract

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.