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arXiv:1202.4697 · Physics Letters A

Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries

Zi-Xiang Hu, Zlatko Papić, Sonika Johri, R. N. Bhatt, Peter Schmitteckert

Published May 16, 2012• 39 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2012.05.031

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We developed a density matrix renormalization group technique to study quantum Hall fractions of fast rotating bosons. In this paper, we present a discussion of the method together with the results which we obtain in three distinct cases of the narrow-channel, cylinder, and spherical geometries. In the narrow-channel case, which is relevant to anisotropic confining traps in the limit of extremely fast rotation, we find a series of zero-temperature phase transitions in the strongly interacting regime as a function of the interaction strength between bosons. We compute energies and density profiles for different filling fractions on a cylinder and compare the convergence rates of the method in the cylinder and a sphere geometries.