Topology in the 2d Heisenberg Model under Gradient Flow

TL;DR

This paper investigates whether the divergence of topological susceptibility in the 2d Heisenberg model persists after applying Gradient Flow, contributing to understanding topological properties in lattice models.

Contribution

It examines the effect of Gradient Flow on the topological susceptibility divergence in the 2d Heisenberg model, a question not previously addressed.

Findings

Gradient Flow reduces topological charge fluctuations

Divergence of susceptibility is mitigated after flow

Provides insights into topological sector behavior

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.