arXiv quant-ph/07020362007-02-14quant-ph

矩阵乘积自旋单链中的纠缠和量子相变

Entanglement and quantum phase transitions in matrix product spin one chains

S. Alipour, V. Karimipour, L. Memarzadeh

发表信息：: Phys. Rev. A 75, 052322 (2007)
DOI：: 10.1103/PhysRevA.75.052322

摘要：

考虑周期链上自旋为1的粒子的单参数矩阵乘积态族，详细研究了这种态的纠缠特性。特别是，我们精确计算了一个网站的纠缠与其余的链，和纠缠的两个遥远的网站与对方，并表明，这两个属性的导数发散时，状态的参数$g$通过一个临界点。这样的点可以被称为量子相变点，因为在该点处，作为哈密顿量的基态的矩阵乘积态的特性不连续地改变。我们还研究了有限尺寸效应，并展示了纠缠如何依赖于链的大小。后一部分与量子计算领域有关，其中量子比特或量子比特的有限阵列中的初始状态准备问题很重要。研究还表明，在临界点附近，两格点纠缠具有标度行为。

英文摘要：

We consider a one-parameter family of matrix product states of spin one particles on a periodic chain and study in detail the entanglement properties of such a state. In particular we calculate exactly the entanglement of one site with the rest of the chain, and the entanglement of two distant sites with each other and show that the derivative of both these properties diverge when the parameter $g$ of the states passes through a critical point. Such a point can be called a point of quantum phase transition, since at this point, the character of the matrix product state which is the ground state of a Hamiltonian, changes discontinuously. We also study the finite size effects and show how the entanglement depends on the size of the chain. This later part is relevant to the field of quantum computation where the problem of initial state preparation in finite arrays of qubits or qutrits is important. It is also shown that entanglement of two sites have scaling behavior near the critical point.

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