Max F. Frenzel, Martin B. Plenio
We present an alternative to the conventional matrix product state representation, which allows us to avoid the local Hilbert space truncation many numerical methods employ, as well as drastically reduce the number of matrices required to describe the state. Utilising chain mappings (linear as well as logarithmic) of the spin-boson model (SBM) Hamiltonian onto a semi-infinite chain, we apply the new method to the sub-ohmic SBM, where we can reproduce many well established features of the quantum phase transition, such as the critical exponent 1/2 predicted by mean-field theory. Via extrapolation of finite-chain results we are able to determine the infinite-chain critical couplings at which the transition occurs.
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http://arxiv.org/abs/1211.3464
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