PoS - Proceedings of Science
Volume 363 - 37th International Symposium on Lattice Field Theory (LATTICE2019) - Main session
Zero modes of the domain wall operator for 2+1 flavor lattices with $a^{-1} \approx 1$ GeV
D. Guo
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Pre-published on: January 04, 2020
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The measurement of the topological properties on the lattices usually requires smearing. In this proceeding, we demonstrate that we can use the zero modes of the domain wall operator to study the topological properties in detail without smearing. We show that the eigenvalues and the chirality properties of the eigenvectors are very similar to those of the Dirac operator with mass term in the continuum. The finite fifth dimension brings the residual mass into the eigenvectors but the eigenvectors can still be used to probe the detailed topological properties. We are able to get the quark bilinear $\sum_{\vec{x},\vec{y}}\langle\bar{q}(\vec{x},t)\gamma_5 q(\vec{y},t)\rangle$ through the eigenvectors which contribute to $m_{\eta}$ and $m_{\eta'}$. $m_{\eta}$ and $m_{\eta'}$ are measured and we expect that we can use the zero modes to improve the measurements.
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