Criticality of the Mean-Field Spin-Boson Model: Boson State Truncation and Its Scaling Analysis

Details Criticality of the Mean-Field Spin-Boson Model: Boson State Truncation and Its Scaling Analysis Criticality of the Mean-Field Spin-Boson Model: Boson State Truncation and Its Scaling Analysis

2010-05-27

arxiv.org/abs/1005.4977v1

Euro. Phys. J. B 78, 127 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

9 pages, 7 figures

Scientific paper

The spin-boson model has nontrivial quantum phase transitions at zero temperature induced by the spin-boson coupling. The bosonic numerical renormalization group (BNRG) study of the critical exponents $\beta$ and $\delta$ of this model is hampered by the effects of boson Hilbert space truncation. Here we analyze the mean-field spin boson model to figure out the scaling behavior of magnetization under the cutoff of boson states $N_{b}$. We find that the truncation is a strong relevant operator with respect to the Gaussian fixed point in $01/2$, the truncation produces no effect. Implications of these findings to the BNRG study are discussed.

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