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

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.

9 pages, 2 figures

References in corpus (15)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Quantum Griffiths effects in itinerant Heisenberg magnets
• Effects of dissipation on a quantum critical point with disorder
• Infinite-randomness quantum critical points induced by dissipation
• Theory of smeared quantum phase transitions
• Percolation quantum phase transitions in diluted magnets
• Infinite randomness fixed point of the superconductor-metal quantum phase transition
• Quantum phase transitions of the diluted O(3) rotor model
• Dissipation effects in random transverse-field Ising chains
• Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath
• Percolation transition and dissipation in quantum Ising magnets
• Influence of superohmic dissipation on a disordered quantum critical point
• Complex critical exponents for percolation transitions in Josephson-junction arrays, antiferromagnets, and interacting bosons