Matrix product state representation without explicit local Hilbert space truncation with applications to the sub-ohmic spin-boson model

We present an alternative to the conventional matrix product state representation, which allows us to avoid the explicit local Hilbert space truncation many numerical methods employ. Utilizing chain mappings corresponding to linear and logarithmic discretizations of the spin-boson model onto a semi-infinite chain, we apply the newmethod to the sub-ohmic spin-boson model. We are able to reproduce many well-established features of the quantum phase transition, such as the critical exponent 12 predicted by mean-field theory. Via extrapolation of finite-chain results, we are able to determine the infinitechain critical couplings αc at which the transition occurs and, in general, study the behaviour of the system well into the localized phase. 3 Author to whom any correspondence should be addressed. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New Journal of Physics 15 (2013) 073046 1367-2630/13/073046+13$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft