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arXiv 1004.2828quant-ph
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连续模型中的关联能和纠缠能隙

Correlation Energy and Entanglement Gap in Continuous Models

L. Martina, G. Ruggeri, G. Soliani

摘要:

我们的目标是阐明无限维希尔伯特空间中两体系统的纠缠与关联能之间的关系。为了这个目的,我们考虑完全可解的Moshinsky模型的两个线性耦合谐振子。此外,对于小的耦合值的基态的纠缠是非线性相关的相关能量,涉及对数或代数校正。然后,寻找纠缠的见证观测值,我们展示了如何给出相关能的物理解释。特别地,我们证明了存在一组可分离态,它们与Hartree-Fock态连续相连,可能与确切的基态有较大的重叠,但也有较大的能量期望值。在这个意义上,相关能提供纠缠间隙,即能量尺度,在该能量尺度下,对1粒子谐波子系统执行的测量可以将系统的基态与任何其他分离态区分开。然而,为了验证的程序的一般性,我们比较了1粒子谐波子系统的Moshinsky的模型的能量分布累积量的情况下,在0温度下的阻尼欧姆浴耦合。

英文摘要:

Our goal is to clarify the relation between entanglement and correlation energy in a bipartite system with infinite dimensional Hilbert space. To this aim we consider the completely solvable Moshinsky's model of two linearly coupled harmonic oscillators. Also for small values of the couplings the entanglement of the ground state is nonlinearly related to the correlation energy, involving logarithmic or algebraic corrections. Then, looking for witness observables of the entanglement, we show how to give a physical interpretation of the correlation energy. In particular, we have proven that there exists a set of separable states, continuously connected with the Hartree-Fock state, which may have a larger overlap with the exact ground state, but also a larger energy expectation value. In this sense, the correlation energy provides an entanglement gap, i.e. an energy scale, under which measurements performed on the 1-particle harmonic sub-system can discriminate the ground state from any other separated state of the system. However, in order to verify the generality of the procedure, we have compared the energy distribution cumulants for the 1-particle harmonic sub-system of the Moshinsky's model with the case of a coupling with a damping Ohmic bath at 0 temperature.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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