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arXiv · 1709.06180

Topology in the 2d Heisenberg Model under Gradient Flow

Ilya O. Sandoval·Wolfgang Bietenholz·Philippe de Forcrand·Urs Gerber·Héctor Mejía-Díaz
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Abstract

The 2d Heisenberg model --- or 2d O(3) model --- is popular in condensed matter physics, and in particle physics as a toy model for QCD. Along with other analogies, it shares with 4d Yang-Mills theories, and with QCD, the property that the configurations are divided in topological sectors. In the lattice regularisation the topological charge $Q$ can still be defined such that $Q \in \mathbb{Z}$. It has generally been observed, however, that the topological susceptibility $\chi_{\rm t} = \langle Q^2 \rangle / V$ does not scale properly in the continuum limit, i.e. that the quantity $\chi_{\rm t} \xi^2$ diverges for $\xi \to \infty$ (where $\xi$ is the correlation length in lattice units). Here we address the question whether or not this divergence persists after the application of the Gradient Flow.

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Ilya O. Sandoval, Wolfgang Bietenholz, Philippe de Forcrand, Urs Gerber, Héctor Mejía-Díaz. 2017-09-18. Topology in the 2d Heisenberg Model under Gradient Flow. https://doi.org/10.1088/1742-6596/912/1/012024

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