Quantum Phase Transitions on Percolating Lattices

TL;DR

This paper investigates how quantum and thermal fluctuations interact on percolating lattices, revealing new universality classes and exact scaling behaviors in quantum phase transitions at the percolation threshold.

Contribution

It introduces the effects of quantum fluctuations on percolation-induced phase transitions, identifying novel universality classes and exact dynamical scaling in two-dimensional systems.

Findings

Quantum fluctuations lead to new universality classes at the percolation quantum phase transition.

Dynamical correlations exhibit nonclassical, exactly determinable scaling in two dimensions.

Thermal fluctuations typically destroy long-range order, but quantum effects produce subtle, distinct behaviors.

Abstract

When a quantum many-particle system exists on a randomly diluted lattice, its intrinsic thermal and quantum fluctuations coexist with geometric fluctuations due to percolation. In this paper, we explore how the interplay of these fluctuations influences the phase transition at the percolation threshold. While it is well known that thermal fluctuations generically destroy long-range order on the critical percolation cluster, the effects of quantum fluctuations are more subtle. In diluted quantum magnets with and without dissipation, this leads to novel universality classes for the zero-temperature percolation quantum phase transition. Observables involving dynamical correlations display nonclassical scaling behavior that can nonetheless be determined exactly in two dimensions.