一维Leinaas-Myrheim任意子的二次量子化及其与Lieb-Liniger模型的关系
Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the Lieb-Liniger model
摘要：
在一维空间中，Leinaas和Myrheim最初描述的任意子形式上等价于Lieb-Liniger模型描述的局部相互作用玻色子。这使得在任意子的背景下对相互作用玻色子进行了有趣的重新解释。我们详细阐述了这种平行，特别是包括多体束缚态的吸引力Lieb-Liniger模型。在任意子的背景下，这些束缚态纯粹是由量子统计吸引力和杜撰的量子统计凝聚体产生的，它比玻色-爱因斯坦凝聚体更鲁棒。我们介绍了目前的任意子的第二量子化形式主义，并构造了广义乔丹-维格纳变换，连接它们的Lieb-Liniger模型的玻色子。
英文摘要：
In one spatial dimension, anyons in the original description of Leinaas and Myrheim are formally equivalent to locally interacting bosons described by the Lieb-Liniger model. This admits an interesting reinterpretation of interacting bosons in the context of anyons. We elaborate on this parallel, particularly including the many-body bound states from the attractive Lieb-Liniger model. In the anyonic context these bound states are created purely by quantum-statistical attraction and coined quantum-statistical condensate, which is more robust than the Bose-Einstein condensate. We introduce the second quantization formalism for the present anyons and construct the generalized Jordan-Wigner transformation that connects them to the bosons of the Lieb-Liniger model.
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