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 predicted by mean-field theory. Via extrapolation of finite-chain results, we are able to determine the infinite-chain critical couplings αc at which the transition occurs and, in general, study the behaviour of the system well into the localized phase.
Highlights
The spin-boson model (SBM) describes a single twolevel system (TLS), a spin, coupled to environmental degrees of freedom represented by a continuous bath of bosonic field modes
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
We demonstrate the usefulness of this approach by applying it to study the properties of the second-order magnetic quantum phase transition of the sub-ohmic SBM and their comparison to an analytical approach based on a variational ansatz [2]
Summary
The spin-boson model (SBM) describes a single twolevel system (TLS), a spin, coupled to environmental degrees of freedom represented by a continuous bath of bosonic field modes. It is one of the most important models for studying the general effects arising when a quantum system is coupled to an environment [1]. Many numerical approaches face challenges near and above the transition to the localised phase This is due to the rapidly rising number of field excitations in the localised phase, which imply that the quantum states of the field modes span an increasingly large subspace of their full Hilbert space. We demonstrate the usefulness of this approach by applying it to study the properties of the second-order magnetic quantum phase transition of the sub-ohmic SBM and their comparison to an analytical approach based on a variational ansatz [2]
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