有限程相互作用量子自旋链中的纠缠熵
Entanglement entropy in quantum spin chains with finite range interaction
摘要：
研究了一类相互作用具有有限射程和平移不变性的一维量子自旋链中基态的纠缠熵。这样的系统可以被认为是XY模型的推广。该链分为两部分：一部分包含第一个连续的L自旋;第二部分包含其余的自旋。在这种情况下，纠缠的熵是两部分的冯诺伊曼熵。在我们的计算的核心是显式评估的领导阶项L趋于无穷大的块Toeplitz矩阵的符号属于一般类的2 × 2矩阵函数的行列式。这种行列式的渐近性是用亏格g >= 1的超椭圆曲线的多维θ-函数来计算的，它进入了Riemann-Hilbert问题的解。这些系统的相变的特征是超椭圆曲线的分支点接近单位圆。在这些情况下，熵会以几何学的方式发散。作为特例，我们还恢复了Jin和Korepin（2004）对XX模型以及Its，Jin和Korepin（2005，2006）对XY模型的熵公式.
英文摘要：
We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY model. The chain is divided in two parts: one containing the first consecutive L spins; the second the remaining ones. In this setting the entropy of entanglement is the von Neumann entropy of either part. At the core of our computation is the explicit evaluation of the leading order term as L tends to infinity of the determinant of a block-Toeplitz matrix whose symbol belongs to a general class of 2 x 2 matrix functions. The asymptotics of such determinant is computed in terms of multi-dimensional theta-functions associated to a hyperelliptic curve of genus g >= 1, which enter into the solution of a Riemann-Hilbert problem. Phase transitions for thes systems are characterized by the branch points of the hyperelliptic curve approaching the unit circle. In these circumstances the entropy diverges logarithmically. We also recover, as particular cases, the formulae for the entropy discovered by Jin and Korepin (2004) for the XX model and Its, Jin and Korepin (2005,2006) for the XY model.
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。
