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

Abstract

Abstract. 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 new method 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 1/2 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. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.