The dissipative phase transition in a pair of coupled noisy two-level systems

Abstract

We study the renormalization group (RG) equations of a pair of spin-boson systems coupled in the z-direction with each other. Each spin is coupled to a different bath of harmonic oscillators. We introduce a systematic adiabatic RG, which generalizes the first-order adiabatic renormalization previously used for the single spin-boson model, and we obtain the flow equations for the tunneling constant, the dissipation strength and the inter-spin coupling up to third order in the tunneling. If one of the two spins is treated as a constant magnetization the other spin is described by a biased spin-boson Hamiltonian. In this case the RG equations we find coincide with the ones obtained via a mapping to a long-range Ising chain. If the whole Ohmic two-spin system is considered the Kosterlitz-Thouless phase transition is replaced by a second-order phase transition. In the case of a sub-Ohmic bath our approach predicts that the two-spin system is always localized.

10+3 pages

References in corpus (13)

• On the Integrability of the Rabi Model
• Non-Markovian effects on the dynamics of entanglement
• Generalized rotating-wave approximation for arbitrarily large coupling
• Fundamental Aspects of Quantum Brownian Motion
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• A variational description of the quantum phase transition in the sub-Ohmic spin-boson model
• Dynamics, Synchronization and Quantum Phase Transitions of Two Dissipative Spins
• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
• Universal conductance of nanowires near the superconductor-metal quantum transition
• Theory of smeared quantum phase transitions
• Dissipation effects in random transverse-field Ising chains
• Dissipative Two-Electron Transfer
• Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath

Cited by in corpus (4)

• Performance Evaluation of the Symmetrical Quasi-Classical Dynamics Method based on Meyer-Miller Mapping Hamiltonian in the Treatment of Site-Exciton Models
• The quantum phase transition and correlations in the multi-spin-boson model
• Variational study of two-impurity spin-boson model with a common Ohmic bath: Ground-state phase transitions
• Bath-engineering magnetic order in quantum spin chains: An analytic mapping approach