2D海森堡模型中的Halfton瞬子再访：沿着拓扑大道
Haldane's Instanton in 2D Heisenberg model revisited: along the Avenue of Topology
摘要：
二维海森堡模型中从Néel相到价键晶体态的非受限量子相变目前仍存在争议。一个关键的问题是量子临界点上的Halfton瞬子的抑制，它驱动自旋子的退禁闭。本文利用$ϕ$ -映射拓扑流理论，从拓扑学的角度重新研究了Halfton瞬子。我们发现这些事件是Néel场$\vec{n}$的时空奇点，相应的拓扑荷是$\vec{n}$围绕奇点的缠绕数，可以用$ϕ$ -映射的Hopf指数和Brouwer度来表示.只有当$ϕ$ -字段不具有零点时，才能保证对触发事件的抑制。此外，在海森堡模型中，由于Berry相位而导致的四极性事件也在这个拓扑论证中重现。
英文摘要：
Deconfined quantum phase transition from Néel phase to Valence bond crystal state in 2D Heisenberg model is under debate nowadays. One crucial issue is the suppression of Haldane's instanton on quantum critical point which drives the spinon deconfined. In this paper, by making use of the $ϕ$-mapping topological current theory, we reexamine the Haldane's instanton in an alternative way along the direction of topology. We find that the the monopole events are space-time singularities of Néel field $\vec{n}$, the corresponding topological charges are the wrapping number of $\vec{n}$ around the singularities which can be expressed in terms of the Hopf indices and Brouwer degrees of $ϕ$-mapping. The suppression of the monopole events can only be guaranteed when the $ϕ$-field possesses no zero points. Moreover, the quadrapolarity of monopole events in the Heisenberg model due to the Berry phase is also reproduced in this topological argument.
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。
