Shimizu Kaoru, Tokura Yasuhiro
NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan.
Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, Ibaraki 305-0006, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062143. doi: 10.1103/PhysRevE.92.062143. Epub 2015 Dec 28.
This paper presents a theoretical framework for analyzing the quantum fluctuation properties of a quantum spin chain subject to a quantum phase transition. We can quantify the fluctuation properties by examining the correlation between the fluctuations of two neighboring spins subject to the quantum uncertainty. To do this, we first compute the reduced density matrix ρ of the spin pair from the ground state |Ψ⟩ of a spin chain, and then identify the quantum correlation part ρ(q) embedded in ρ. If the spin chain is translationally symmetric and characterized by a nearest-neighbor two-body spin interaction, we can determine uniquely the form of ρ(q) as W|Φ〉〈Φ| with the weight W ≤1, and quantify the fluctuation properties using the two-spin entangled state |Φ〉. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.
本文提出了一个用于分析处于量子相变的量子自旋链的量子涨落特性的理论框架。我们可以通过研究受量子不确定性影响的两个相邻自旋的涨落之间的相关性来量化涨落特性。为此，我们首先从自旋链的基态|Ψ⟩计算自旋对的约化密度矩阵ρ，然后识别嵌入在ρ中的量子关联部分ρ(q)。如果自旋链是平移对称的且由最近邻两体自旋相互作用表征，我们可以唯一地确定ρ(q)的形式为W|Φ〉〈Φ|，其中权重W≤1，并使用两自旋纠缠态|Φ〉来量化涨落特性。我们展示了横向场量子伊辛自旋链的框架，并指出其对更一般的自旋链模型的有效性。
