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

Ralf Bulla·Ning-Hua Tong·Matthias Vojta
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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.

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Ralf Bulla, Ning-Hua Tong, Matthias Vojta. 2003-10-28. Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model. https://doi.org/10.1103/physrevlett.91.170601

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