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The sub-ohmic spin-boson model exhibits an interesting and much-studied quantum phase transition from a delocalized phase at weak spin-bath coupling to a localized phase at strong coupling. Previous works using NRG to calculate the critical exponents of this model near the phase transition failed partly because NRG cannot deal with the large number of states per bath oscillator required to describe the localized phase [1]. We show how this problem can be overcome by using DMRG to construct, for each site of the Wilson chain, an optimized boson basis containing only a small number of states, and using the resulting basis for standard NRG calculations. For s<1/2, our results are in good agreement with mean-field predictions for the critical exponents.
[1] M. Vojta, N.-H. Tong, R. Bulla, Quantum Phase Transitions in the Sub-Ohmic Spin-Boson Model: Failure of the Quantum-Classical Mapping, Phys. Rev. Lett. 94, 070604 (2005); Erratum: Phys. Rev. Lett., 102, 249904 (2009) |
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