θvacuum effects on chiral condensation and theη′meson correlators in two-flavor massiveQED2on the lattice

We study the scalar and pseudoscalar condensates and the ${\eta }^{\prime }$ meson correlators of the two-flavor massive Schwinger model in the $\theta \ne 0$ vacuum. Exploiting our new method which was developed to investigate topological effects in the previous work, we find that $\langle \overline{\psi }{\gamma }_5\psi {\rangle }^{\theta }\ne 0$ and there exists a long-range correlation of the ${\eta }^{\prime }$ meson. This phenomenon is well described by the clustering property. We also find that even in $\theta =0$ case the cancellation of the long-range correlation is nontrivial and requires accurate contributions from higher topological sectors. Our results imply that the fluctuation of the disconnected diagram originates from the pseudoscalar condensate in each topological sector.