Dynamics of the sub-Ohmic spin-boson model : a comparison of three numerical approaches
Date of Issue2013
School of Materials Science and Engineering
Dynamics of the sub-Ohmic spin-boson model is examined using three numerical approaches, namely the Dirac-Frenkel time-dependent variation with the Davydov D1 ansatz, the adaptive time-dependent density matrix renormalization group method within the representation of orthogonal polynomials, and a perturbative approach based on a unitary transformation. In order to probe the validity regimes of the three approaches, we study the dynamics of a qubit coupled to a bosonic bath with and without a local ﬁeld. Comparison of the up-state population evolution shows that the three approaches are in agreement in the weak-coupling regime but exhibit marked differences when the coupling strength is large. The Davydov D1 ansatz and the time-dependent density matrix renormalization group can both be reliably employed in the weak-coupling regime, while the former is also valid in the strong-coupling regime as judged by how faithfully the trial state follows the Schrodinger ¨ equation. We further explore the bipartite entanglement dynamics between two qubits coupled with individual bosonic baths which reveals entanglement sudden death and revival.
Physical review E
© 2013 American Physical Society. This paper was published in Physical Review E - Statistical, Nonlinear, and Soft Matter Physics and is made available as an electronic reprint (preprint) with permission of American Physical Society. The paper can be found at the following official DOI: [http://dx.doi.org/10.1103/PhysRevE.88.023303]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.