Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation

TL;DR

This paper studies how sub-Ohmic dissipation affects quantum phase transitions in diluted quantum Ising and rotor models, revealing a transition characterized by frozen clusters and inhomogeneous magnetic phases.

Contribution

It introduces a detailed analysis of the impact of sub-Ohmic dissipation on percolation-driven quantum phase transitions, highlighting the emergence of frozen clusters and smeared transitions.

Findings

Quantum dynamics of large clusters freeze due to dissipation

Identification of a new phase separating super-paramagnetic and ferromagnetic states

Comparison of sub-Ohmic, Ohmic, and super-Ohmic dissipation effects

Abstract

We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.