Success and failure of the plasma analogy for Laughlin states on a torus

摘要: We investigate the nature of plasma analogy for Laughlin wave function on a torus describing quantum Hall plateau at $\nu=\frac{1}{q}$. first establish, as expected, that is screening if there are no short nontrivial paths around torus. also find when one handles has circumference -- i.e. thin-torus limit longer screens. To quantify this we compute normalization state, both numerically and analytically. For numerical calculation expand state in Fock basis slater-determinants single particle orbitals, determine coefficients expansion geometry. In thin only few configurations have non-zero coefficients, their analytical forms simplify greatly. Using simple limit, can reconstruct analytically extend it back into 2D regime. geometry dependent corrections to normalization, turn implies not limit. Further obtain an approximate factor gives good description all tori, by extrapolating thick