Dynamics of the sub-Ohmic spin-boson model: a comparison of three numerical approaches.
Dynamics of the sub-Ohmic spin-boson model: a comparison of three numerical approaches.
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DOI：
10.1103/physreve.88.023303
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
Yao Yao-Yao;Liwei Duan;Z. Lü;Chang-qin Wu;Yang Zhao
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文献类型：
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作者：
Yao Yao-Yao;Liwei Duan;Z. Lü;Chang-qin Wu;Yang Zhao
用三种数值方法研究了亚欧姆自旋玻色子模型的动力学，即用Davydov D（1）模型的Dirac Frenkel含时变分方法、正交多项式表示的自适应含时密度矩阵重整化群方法和基于幺正变换的微扰方法.为了探讨这三种方法的有效性机制，我们研究了耦合到玻色子浴的量子比特在有和没有局域场的情况下的动力学。对上态布居演化的比较表明，这三种方法在弱耦合区是一致的，但在耦合强度较大时表现出明显的差异。Davydov D（1）近似和含时密度矩阵重整化群都可以可靠地用于弱耦合区，而前者在强耦合区也是有效的，这取决于试验态是否忠实地遵循薛定谔方程。我们进一步探讨了两个量子比特之间的纠缠动力学，并结合单独的玻色子浴，揭示了纠缠的突然死亡和复活。
Dynamics of the sub-Ohmic spin-boson model is examined using three numerical approaches, namely the Dirac-Frenkel time-dependent variation with the Davydov D(1) 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 D(1) 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 Schrödinger equation. We further explore the bipartite entanglement dynamics between two qubits coupled with individual bosonic baths which reveals entanglement sudden death and revival.