Quadrupolar quantum criticality on a fractal

TL;DR

This paper investigates the quantum critical behavior of quadrupolar $S=1$ magnets on a fractal lattice, revealing a unique quantum critical point at the percolation threshold driven by quantum fluctuations and disorder.

Contribution

It uncovers a novel quantum critical point in quadrupolar magnets on a fractal, distinct from dipolar systems, highlighting the interplay of quantum fluctuations and randomness.

Findings

Quadrupolar magnets are quantum disordered at the percolation threshold.

Long-range quadrupolar order exists for all $p<p^*$ and vanishes at $p^*$.

Evidence of scaling behavior indicates an unusual quantum criticality.

Abstract

We study the ground state ordering of quadrupolar ordered $S=1$ magnets as a function of spin dilution probability $p$ on the triangular lattice. In sharp contrast to the ordering of $S=1/2$ dipolar N\'eel magnets on percolating clusters, we find that the quadrupolar magnets are quantum disordered at the percolation threshold, $p=p^*$. Further we find that long-range quadrupolar order is present for all $p<p^*$ and vanishes first exactly at $p^*$. Strong evidence for scaling behavior close to $p^*$ points to an unusual quantum criticality without fine tuning that arises from an interplay of quantum fluctuations and randomness.