Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model

2003/06/30 by Ralf Bulla, Ning-Hua Tong, Matthias Vojta · 2 citations
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevlett.91.170601

published as Phys. Rev. Lett. 91, 170601 (2003) · 4 pages, 5 figs, (v2) final version as published

arxiv created 2003/10/28 · arxiv updated 2009/11/30

Abstract

We describe the generalization of Wilson's Numerical Renormalization Group method to quantum impurity models with a bosonic bath, providing a general non-perturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) ~ omega^s. We find clear evidence for a line of continuous quantum phase transitions for subohmic bath exponents 0<s<1; the line terminates in the well-known Kosterlitz-Thouless transition at s=1. Contact is made with results from perturbative renormalization group, and various other applications are outlined.

Cited by

• Quantum phase transition of sub-Ohmic spin-boson models: An approach by the multiple Davydov D2 Ansatz
• Hierarchical Equations of Motion Solved with the Multiconfigurational Ehrenfest Ansatz

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