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 ${\chi }_{\mathrm{t}}=⟨Q^2⟩/V$ does not scale properly in the continuum limit, i.e. that the quantity ${\chi }_{\mathrm{t}}{\xi }^2$ 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.

arXiv comment10 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)

References in corpus (8)

• Properties and uses of the Wilson flow in lattice QCD
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• Topological effects in QCD and the problem of short-distance singularities
• Universality of the topological susceptibility in the SU(3) gauge theory
• Topological susceptibility in full QCD with Ginsparg-Wilson fermions
• Instantons and the fixed point topological charge in the two-dimensional O(3) sigma-model
• Topological Lattice Actions
• Measuring the Topological Susceptibility in a Fixed Sector

Cited by in corpus (1)

• Topological Susceptibility of the 2d O(3) Model under Gradient Flow