Dissipative spin dynamics near a quantum critical point: Numerical Renormalization Group and Majorana diagrammatics

Abstract

We provide an extensive study of the sub-ohmic spin-boson model with power law density of states J(ω)=ω^s (with 0<s<1), focusing on the equilibrium dynamics of the three possible spin components, from very weak dissipation to the quantum critical regime. Two complementary methods, the bosonic Numerical Renormalization Group (NRG) and Majorana diagrammatics, are used to explore the physical properties in a wide range of parameters. We show that the bosonic self-energy is the crucial ingredient for the description of critical fluctuations, but that many-body vertex corrections need to be incorporated as well in order to obtain quantitative agreement of the diagrammatics with the numerical simulations. Our results suggest that the out-of-equilibrium dynamics in dissipative models beyond the Bloch-Redfield regime should be reconsidered in the long-time limit. Regarding also the spin-boson Hamiltonian as a toy model of quantum criticality, some of the insights gained here may be relevant for field theories of electrons coupled to bosons in higher dimensions.

19 pages, 19 figures. Minor changes in V2

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• Numerical Renormalization Group for the sub-ohmic spin-boson model: A conspiracy of errors
• Majorana representation for dissipative spin systems
• Nonequilibrium spin-boson model: from weak to strong coupling
• Dynamics of a Qubit in a High-Impedance Transmission Line from a Bath Perspective
• Using Majorana spin-1/2 representation for the spin-boson model
• Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models
• Microwave Scattering in the Subohmic Spin-Boson Systems of Superconducting Circuits
• Green's functions for spin boson systems: Beyond conventional perturbation theories
• Quantum correlation functions through tensor network path integral
• Magnetotransport in the Kondo model with ferromagnetic exchange interaction
• Equilibrium Dynamics of the Sub-Ohmic Spin-boson Model At Finite Temperature
• Equilibrium Dynamics of the Sub-Ohmic Spin-boson Model Under Bias
• No spin-localization phase transition in the spin-boson model without local field
• Single Mode Approximation for sub-Ohmic Spin-Boson Model: Adiabatic Limit and Critical Properties