Localization of topological charge density near Tc in quenched QCD with Wilson flow

Abstract

We smear quenched lattice QCD ensembles with lattice volume 32 3 × 8 by using Wilson flow. Six ensembles at temperature near the critical temperature T c corresponding to the critical inverse coupling β c ¼ 6.06173ð49Þ are used to investigate the localization of topological charge density. If the effective smearing radius of Wilson flow is large enough, the density, size and peak of Harrington-Shepard (HS) caloron-like topological lumps of ensembles are stable when β ≤ 6.050, but start to change significantly when β ≥ 6.055. The inverse participation ratio (IPR) of topological charge density shows similar results, it begins to increase when β ≥ 6.055 and is stable when β ≤ 6.050. The pseudoscalar glueball mass is extracted from the topological charge density correlator (TCDC) of ensembles at T ¼ 1.19T c , and 1.36T c , the masses are 1.915(98) and 1.829(123) GeV respectively, they are consistent with results from conventional methods.

Study of the topological quantities of lattice QCD using a modified DCGAN frame

“…Next, the 4D M-DCGAN frame is applied to directly generate the topological charge density in lattice QCD using 300 training data of topological charge density, with used to train the model of the 4D M-DCGAN. The input of the generator for the 4D M-DCGAN is a random latent variable tensor with shape [-1, 100], and the output is a tensor with shape [-1, 1, 24,12,12,12]. For example, we generate a topological charge density tensor with the shape [24,12,12,12].…”

“…The input of the generator for the 4D M-DCGAN is a random latent variable tensor with shape [-1, 100], and the output is a tensor with shape [-1, 1, 24,12,12,12]. For example, we generate a topological charge density tensor with the shape [24,12,12,12]. The input shape is [1,100], and the output shape is [1,1,24,12,12,12].…”

“…For example, we generate a topological charge density tensor with the shape [24,12,12,12]. The input shape is [1,100], and the output shape is [1,1,24,12,12,12]. Finally, the output must be reshaped into the tensor with shape [24,12,12,12].…”

“…The input shape is [1,100], and the output shape is [1,1,24,12,12,12]. Finally, the output must be reshaped into the tensor with shape [24,12,12,12]. The visualization is referenced from the paper [33] and PyVista [34].…”