arXiv quant-ph/06121942006-12-22quant-ph

相互作用自旋链中的几何相位和临界现象

Geometric Phases and Critical Phenomena in a Chain of Interacting Spins

M. E. Reuter, M. J. Hartmann, M. B. Plenio

备注：: 7 Figures
发表信息：: Proc. Roy. Soc. Lond. A 463, 1271 (2007)
DOI：: 10.1098/rspa.2007.1822

摘要：

几何相位可以作为相互作用自旋链的临界区域的特征，在极限情况下，参数空间中相应的回路收缩到一个点，自旋的数量扩展到无穷大;对于有限的回路半径或有限的自旋链长度，几何相位总是平凡的（2 π的倍数）。在这项工作中，相比之下，提出了两个相关的签名的临界遵守有限尺寸标度和规避需要假设任何非物理限制。它们是基于巴格曼不变量的概念，其相位可被视为贝里相位的离散化版本。作为电路被认为是由一个离散的，有限的一组顶点在参数空间中，他们能够直接通过一个临界点，而不是必须circumnavigate it. The建议的机制被证明是提供一个诊断工具的情况下，一个给定的不可解的一维自旋链与最近邻相互作用的存在下，外部磁场的临界性。

英文摘要：

The geometric phase can act as a signature for critical regions of interacting spin chains in the limit where the corresponding circuit in parameter space is shrunk to a point and the number of spins is extended to infinity; for finite circuit radii or finite spin chain lengths, the geometric phase is always trivial (a multiple of 2pi). In this work, by contrast, two related signatures of criticality are proposed which obey finite-size scaling and which circumvent the need for assuming any unphysical limits. They are based on the notion of the Bargmann invariant whose phase may be regarded as a discretized version of Berry's phase. As circuits are considered which are composed of a discrete, finite set of vertices in parameter space, they are able to pass directly through a critical point, rather than having to circumnavigate it. The proposed mechanism is shown to provide a diagnostic tool for criticality in the case of a given non-solvable one-dimensional spin chain with nearest-neighbour interactions in the presence of an external magnetic field.

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摘要：

英文摘要：

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