Smeared nematic quantum phase transitions due to rare-region effects in inhomogeneous systems

TL;DR

This paper explores how inhomogeneities and rare-region effects lead to smeared quantum nematic transitions, creating an extended nematic phase separate from the density-wave transition in disordered systems.

Contribution

It demonstrates that rare droplets induce a smeared nematic transition, revealing a new inhomogeneous phase structure in disordered quantum systems.

Findings

Rare droplets sustain long-range nematic order but not density-wave order.

Moderately large droplets undergo a second-order nematic transition before the main transition.

A smeared quantum nematic transition emerges, separated from the density-wave transition.

Abstract

The concept of a vestigial nematic order emerging from a "mother" spin or charge density-wave state has been applied to describe the phase diagrams of several systems, including unconventional superconductors. In a perfectly clean system, the two orders appear simultaneously via a first-order quantum phase transition, implying the absence of quantum criticality. Here, we investigate how this behavior is affected by impurity-free droplets that are naturally present in inhomogeneous systems. Due to their quantum dynamics, finite-size droplets sustain long-range nematic order but not long-range density-wave order. Interestingly, rare droplets with moderately large sizes undergo a second-order nematic transition even before the first-order quantum transition of the clean system. This gives rise to an extended regime of inhomogeneous nematic order, which is followed by a density-wave quantum Griffiths phase. As a result, a smeared quantum nematic transition, separated from the density-wave quantum transition, emerges in moderately disordered systems.