Strong randomness criticality in the scratched-XY model

TL;DR

This paper investigates a modified 2D XY model with power-law disorder, revealing a new type of superfluid transition driven by strong randomness, characterized by a non-universal superfluid stiffness jump, supported by semi-renormalization group theory.

Contribution

It introduces the scratched-XY criticality, a novel superfluid transition mechanism caused by strong disorder, and provides numerical evidence using a minimal finite size effect model.

Findings

Existence of scratched-XY criticality at finite temperature

Non-universal jump in superfluid stiffness

Agreement with semi-renormalization group theory

Abstract

We study the finite-temperature superfluid transition in a modified two-dimensional (2D) XY model with power-law distributed "scratch"-like bond disorder. As its exponent decreases, the disorder grows stronger and the mechanism driving the superfluid transition changes from conventional vortex-pair unbinding to a strong randomness criticality (termed scratched-XY criticality) characterized by a non-universal jump of the superfluid stiffness. The existence of the scratched-XY criticality at finite temperature and its description by an asymptotically exact semi-renormalization group theory, previously developed for the superfluid-insulator transition in one-dimensional disordered quantum systems, is numerically proven by designing a model with minimal finite size effects. Possible experimental implementations are discussed.