Reply to “Comment on Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement”
Reply to “Comment on Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement”
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发表时间：
2005
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通讯作者：
J. Reslen;L. Quiroga;N. F. Johnson
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作者：
J. Reslen;L. Quiroga;N. F. Johnson
我们的信[1]表明，在描述量子比特约化子系统的有效哈密顿量水平上，迪凯模型和无限程XX（Lipkin）模型之间存在等价性。Brankov等人的评论断言，与他们以前报道的结果相比，我们用约化的哈密顿量代替原来的迪凯哈密顿量是“错误的”。Brankov等人“的批评是错误的-简而言之，他们使用“错误”这个词是错误的，因为我们没有声明，在我们的信中的任何地方，声称我们的有效（即约化）量子位哈密顿量在有限温度下是精确的。然而，正是在这个基础上，也只有在这个基础上，Brankov等人才使用“错误”一词。我们的信没有任何问题。作为旁注，我们强调他们自己早期的工作实际上与我们论文的核心结果无关。此外，在Brankov等人的评论中还有其他一些令人困惑的陈述，为了完整起见，我们在下面指出。首先，我们这封信的目标是研究量子比特子系统的纠缠特征，而不是整个量子比特辐射系统。我们专注于量子相变，根据定义，发生在零温度。特别是，我们研究了两量子比特纠缠的有限尺寸标度，并将其与之前发表的完整迪凯哈密顿量的数值结果进行了对比[2]。我们的主要发现是，即使在最低阶近似的水平（即求和所有累积量的特殊部分），我们的约化有效哈密顿量在零温度下产生的量子相变在相同的临界耦合常数作为完整的迪凯哈密顿量。更重要的是，我们的约化有效哈密顿量显示了两量子比特纠缠（即并发）的相同临界有限尺寸标度指数。此外，我们还找到了一个普适的尺度函数。第二，在我们的信中，我们没有对布兰科夫等人提出异议。s声称，我们的温度相关的哈密顿（方程。(8)[1]不准确。显然不是。相反，如前所述，
Our Letter [1] shows that there is an equivalence between the Dicke model and the infinitely range XX (Lipkin) model, at the level of the effective Hamiltonian describing the qubit reduced subsystem. The Comment by Brankov et al. asserts that our use of a reduced Hamiltonian in place of the original Dicke Hamiltonian, is “wrong” as compared to the results which they previously reported. Brankov et al.’s criticism is misguided – in short, they are wrong to use the word “wrong” since we make no statement, anywhere in our Letter, to claim that our effective (i.e. reduced) qubit Hamiltonian is exact at finite temperatures. Yet it is on this basis, and this basis alone, that Brankov et al. use the word “wrong”. There is nothing wrong with our Letter. As a side note, we emphasize that their own earlier work is effectively irrelevant to the core results of our paper. In addition, there are several other confused statements in the Comment by Brankov et al. which, for the sake of completeness, we point out below. First, the goal of our Letter was to study the entanglement features of the qubit subsystem, not the entire qubit-radiation system. We focused on the quantum phase transition which, by definition, occurs at zero temperature. In particular, we looked at the finite-size scaling of two-qubit entanglement and contrasted it with previously published numerical results for the full Dicke Hamiltonian [2]. Our main finding was that even at the level of the lowest-order approximation (i.e. summing special parts of all cumulants) our reduced effective Hamiltonian at zero temperature yields a quantum phase transition at the same critical coupling constant as the full Dicke Hamiltonian. Even more importantly, our reduced effective Hamiltonian shows the same critical finite-size scaling exponents for two-qubit entanglement (i.e. concurrence). In addition, we found a universal scaling function for the behavior of the concurrence. Second, at no point in our Letter do we dispute Brankov et al.’s claim that our temperaturedependent Hamiltonian (Eq.(8) in [1]) is not exact. Obviously it is not. Instead, and as stated,