Numerical Renormalization Group for the sub-ohmic spin-boson model: A conspiracy of errors

Abstract

The application of Wilson's Numerical Renormalization Group (NRG) method to dissipative quantum impurity models, in particular the sub-ohmic spin-boson model, has led to conclusions regarding the quantum critical behavior which are in disagreement with those from other methods and which are by now recognized as erroneous. The errors of NRG remained initially undetected because NRG delivered an internally consistent set of critical exponents satisfying hyperscaling. Here we discuss how the conspiracy of two errors - the Hilbert-space truncation error and the mass-flow error - could lead to this consistent set of exponents. Remarkably, both errors, albeit of different origin, force the system to obey naive scaling laws even when the physical model violates naive scaling. In particular, we show that a combination of the Hilbert-space truncation and mass-flow errors induce an artificial non-analytic term in the Landau expansion of the free energy which dominates the critical behavior for bath exponents s<1/2.

9 pages, 3 figs

References in corpus (15)

• The numerical renormalization group method for quantum impurity systems
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model
• Phase transitions in the pseudogap Anderson and Kondo models: Critical dimensions, renormalization group, and local-moment criticality
• A variational description of the quantum phase transition in the sub-Ohmic spin-boson model
• Entanglement and Criticality in Quantum Impurity Systems
• Upper-critical dimension in a quantum impurity model: Critical theory of the asymmetric pseudogap Kondo problem
• Quantum critical properties of the Bose-Fermi Kondo Model in a large-N limit
• Kondo physics and dissipation: A numerical renormalization-group approach to Bose-Fermi Kondo models
• Density matrix renormalization group approach of the spin-boson model
• Finite Size Scaling of Classical Long-Ranged Ising Chains and the Criticality of Dissipative Quantum Impurity Models
• Dissipative spin dynamics near a quantum critical point: Numerical Renormalization Group and Majorana diagrammatics
• Quantum criticality of the sub-ohmic spin-boson model
• Quantum phase transition in the spin boson model
• Quantum phase transition of the sub-Ohmic rotor model

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