Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/11143
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Type: Journal article
Title: Numerical study of the lattice index theorem using improved cooling and overlap fermions
Author: Zhang, J.
Bilson-Thompson, S.
Bonnet, F.
Leinweber, D.
Williams, A.
Zanotti, J.
Citation: Physical Review. D. Particles, Fields, Gravitation and Cosmology, 2002; 65(7):074510-1-074510-7
Publisher: American Physical Soc
Issue Date: 2002
ISSN: 1550-7998
0556-2821
Organisation: Centre for the Sub-Atomic Structure of Matter
Statement of
Responsibility: 
J. B. Zhang, S. O. Bilson-Thompson, F. D. R. Bonnet, D. B. Leinweber, A. G. Williams, and J. M. Zanotti
Abstract: We investigate the topological charge and the index theorem on finite lattices numerically. Using mean field improved gauge-field configurations we calculate the topological charge Q using the gluon field definition with O(a⁴)-improved cooling and an O(a⁴)-improved field strength tensor Fμν. We also calculate the index of the massless overlap fermion operator by directly measuring the differences between the numbers of zero modes with left- and right–handed chiralities. For sufficiently smooth field configurations we find that the gluon field definition of the topological charge is an integer to better than 1%, and furthermore that this agrees with the index of the overlap Dirac operator, i.e., the Atiyah-Singer index theorem is satisfied. This establishes a benchmark for reliability when calculating lattice quantities that are very sensitive to topology.
Rights: ©2002 American Physical Society
RMID: 0020020657
DOI: 10.1103/PhysRevD.65.074510
Appears in Collections:Special Research Centre for the Subatomic Structure of Matter publications

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