The Slab Method to Measure the Topological Susceptibility

Abstract

In simulations of a model with topological sectors, algorithms which proceed in small update steps tend to get stuck in one sector, especially on fine lattices. This distorts the numerical results; in particular it is not straightforward to measure the topological susceptibility χ t . We test a method to measure χ t even if configurations from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as "slabs". This enables the evaluation of χ t , as we demonstrate with numerical results for non-linear σ -models and for 2-flavour QCD. In the latter case, the gradient flow is applied for the smoothing of the gauge configurations, and the slab method results for χ t are stable over a broad range of flow times.34th International Symposium on Lattice Field Theory 1 Typically Q 2 > 1 is required, and one should only involve sectors with small |Q|.

Massive Schwinger model at finite θ

“…In fact euclidean lattice gauge theory, our main non-perturbative tool for studying QCD from first principles, has not been able to help us much because of the imaginary contribution to the action coming from the θ term, that prevents the applicability of the importance sampling method [5]. This is the main reason why the only progress in the analysis of the finite * Corresponding author: eduroyo@unizar.es temperature θ dependence of the vacuum energy density in pure gauge QCD, outside of approximations, reduces to the computation of the first few coefficients in the expansion of the free energy density in powers of θ [6], and the situation in full QCD with dynamical fermions is, on the other hand, even worse [7][8][9][10][11][12].…”

Topological Susceptibility under Gradient Flow

“…where c is a constant (with respect to x), which increases roughly like 0.38 √ t [19]. The fits (5), in the sectors |Q| ≤ 2, at different instances of the GF time, lead to the results for the topological susceptibility χ t in the plot on the right.…”

“…The slab method has been tested in 2-flavour QCD, with twisted-mass quarks and the Wilson gauge action, in a volume 16 3 × 32, at β = 3.9 and bare mass 0.015, which corresponds to a pion mass of m π 650 MeV and a lattice spacing a 0.079 fm [18,19].…”

New simulation strategies for lattice gauge theory

“…Studies were performed for both pure SU(3) gauge theory, as demonstrated in Fig. 9 (right), and for two color QCD with two heavy quark flavors [am π = 0.4446 (6) and a f π = 0.1001 (18)], as demonstrated in Fig. 10.…”

“…In the next sections, I briefly review these strategies, as well as highlight some of their advantages and drawbacks (also see [15,16,17] for further discussion of these approaches, as presented at this conference). It should be mentioned that a number of strategies have been discussed at this conference which address topological freezing from an analysis standpoint rather from the standpoint of gauge generation [18,19]. Although these are very interesting and import works, they will not be discussed here in any detail.…”