二聚量子自旋系统的路径积分
Path integrals for dimerized quantum spin systems
摘要：
二聚化的量子自旋系统可以在几种情况下出现，例如通过空间中反铁磁交换耦合的调制，或者在受抑的量子反铁磁体中。一般来说，这样的系统显示出作为合适的耦合常数的函数的到Néel状态的量子相变。我们在这里提出了两个路径积分公式适用于自旋$S=1/2$二聚体系。第一个是描述SO（4）流形中的二聚体自由度，第二个是Sachdev和Bhatt引入的键算子的路径积分。路径积分量子化是使用约束系统的Faddeev-Jackiw辛形式主义进行的，使得在这两种情况下都提供了从算子的代数产生的度量和约束。作为一个例子，我们考虑一个自旋佩尔斯链，并说明如何达到相应的场论，从SO（4）公式和键算符开始。
英文摘要：
Dimerized quantum spin systems may appear under several circumstances, e.g\ by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase transition to a Néel state as a function of a suitable coupling constant. We present here two path-integral formulations appropriate for spin $S=1/2$ dimerized systems. The first one deals with a description of the dimers degrees of freedom in an SO(4) manifold, while the second one provides a path-integral for the bond-operators introduced by Sachdev and Bhatt. The path-integral quantization is performed using the Faddeev-Jackiw symplectic formalism for constrained systems, such that the measures and constraints that result from the algebra of the operators is provided in both cases. As an example we consider a spin-Peierls chain, and show how to arrive at the corresponding field-theory, starting with both a SO(4) formulation and bond-operators.
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