A numerical finite size scaling approach to many-body localization

Details A numerical finite size scaling approach to many-body localization A numerical finite size scaling approach to many-body localization

2007-09-14

arxiv.org/abs/0709.2244v1

Phys. Rev. Lett. 100, 076602 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.100.076602

We develop a numerical technique to study Anderson localization in interacting electronic systems. The ground state of the disordered system is calculated with quantum Monte-Carlo simulations while the localization properties are extracted from the ``Thouless conductance'' $g$, i.e. the curvature of the energy with respect to an Aharonov-Bohm flux. We apply our method to polarized electrons in a two dimensional system of size $L$. We recover the well known universal $\beta(g)=\rm{d}\log g/\rm{d}\log L$ one parameter scaling function without interaction. Upon switching on the interaction, we find that $\beta(g)$ is unchanged while the system flows toward the insulating limit. We conclude that polarized electrons in two dimensions stay in an insulating state in the presence of weak to moderate electron-electron correlations.

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