Matrix Product State Representation without explicit local Hilbert Space Truncation with Applications to the Sub-Ohmic Spin-Boson Model

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. Utilising 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 SBM. 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 infinite-chain critical couplings at which the transition occurs and, in general, study the behaviour of the system well into the localised phase.

8 pages, 8 figures

References in corpus (3)

• The numerical renormalization group method for quantum impurity systems
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Critical and strong-coupling phases in one- and two-bath spin-boson models

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• Unveiling quantum entanglement and correlation of sub-Ohmic and Ohmic baths for quantum phase transitions in dissipative systems
• Quantum tricritical point emerging in the spin-boson model with two dissipative spins in staggered biases
• Quantum criticality of the Ohmic spin-boson model in a high dense spectrum: symmetries,quantum fluctuations and correlations
• Crucial effect of transverse vibrations on the transport through polymer chains
• Numerical variational simulations of quantum phase transitions in the sub-Ohmic spin-boson model with multiple polaron ansatz
• Impurity-Induced Environmental Quantum Phase Transitions in the Quadratic-Coupling Spin-Boson Model
• Quantum criticality in sub-Ohmic systems with three competing terms: beyond conventional spin-boson physics