Papers › Winding number on 3D lattice
Winding number on 3D lattice
Okuto Morikawa, Hiroshi Suzuki
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We propose a simple numerical method which computes an approximate value of the winding number of a mapping from 3D torus~T³ to the unitary group~U(N), when T³ is approximated by discrete lattice points. Our method consists of a ``tree-level improved'' discretization of the winding number and the gradient flow associated with an ``over-improved'' lattice action. By employing a one-parameter family of mappings from T³ to SU(2) with known winding numbers, we demonstrate that the method works quite well even for coarse lattices, reproducing integer winding numbers in a good accuracy. Our method can trivially be generalized to the case of higher-dimensional tori.
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