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Haldane’s instanton in 2D Heisenberg model revisited: Along the avenue of topology. (English) Zbl 1236.82099

Summary: 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 Letter, by making use of the \(\varphi \)-mapping topological current theory, we reexamine the Haldane’s instanton in an alternative way along the direction of topology. We find that the monopole events are space-time singularities of Néel field \(\vec{n}\), the corresponding topological charges are the wrapping number \(\vec{n}\) of around the singularities which can be expressed in terms of the Hopf indices and Brouwer degrees of \(\varphi \)-mapping. The suppression of the monopole events can only be guaranteed when the \(\varphi \)-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.

MSC:

82D40 Statistical mechanics of magnetic materials
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B27 Critical phenomena in equilibrium statistical mechanics
82D20 Statistical mechanics of solids
82D25 Statistical mechanics of crystals
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
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