Topology in the 2d Heisenberg Model under Gradient Flow

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 $χ_{\rm t} = \langle Q^2 \rangle / V$ does not scale properly in the continuum limit, i.e. that the quantity $χ_{\rm t} ξ^2$ diverges for $ξ\to \infty$ (where $ξ$ 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.

10 pages, LaTex, 7 figures, 2 tables, talk presented at the XXXI Reunión Anual de la División de Partículas y Campos de la Sociedad Mexicana de Física (CINVESTAV, Mexico City)