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We investigate the nature of the plasma analogy for the Laughlin wave function on a torus describing the quantum Hall plateau at $ u=frac{1}{q}$. We first establish, as expected, that the plasma is screening if there are no short nontrivial paths around the torus. We also find that when one of the handles has a short circumference -- i.e. the thin-torus limit -- the plasma no longer screens. To quantify this we compute the normalization of the Laughlin state, both numerically and analytically. For the numerical calculation we expand the Laughlin state in a Fock basis of slater-determinants of single particle orbitals, and determine the Fock coefficients of the expansion as a function of torus geometry. In the thin torus limit only a few Fock configurations have non-zero coefficients, and their analytical forms simplify greatly. Using this simple limit, we can reconstruct the normalization and analytically extend it back into the 2D regime. We find that there are geometry dependent corrections to the normalization, and this in turn implies that the plasma in the plasma analogy is not screening when in the thin torus limit. Further we obtain an approximate normalization factor that gives a good description of the normalization for all tori, by extrapolating the thin torus normalization to the thick torus limit.
We study lattice wave functions obtained from the SU(2)$_1$ Wess-Zumino-Witten conformal field theory. Following Moore and Reads construction, the Kalmeyer-Laughlin fractional quantum Hall state is defined as a correlation function of primary fields.
We develop a method to efficiently calculate trial wave functions for quantum Hall systems which involve projection onto the lowest Landau level. The method essentially replaces lowest Landau level projection by projection onto the $M$ lowest eigenst
We use conformal field theory to construct model wavefunctions for a gapless interface between latti
We conjecture that the counting of the levels in the orbital entanglement spectra (OES) of finite-sized Laughlin Fractional Quantum Hall (FQH) droplets at filling $ u=1/m$ is described by the Haldane statistics of particles in a box of finite size. T
Interfaces between topologically distinct phases of matter reveal a remarkably rich phenomenology. We study the experimentally relevant interface between a Laughlin phase at filling factor $ u=1/3$ and a Halperin 332 phase at filling factor $ u=2/5$.