A numerical finite size scaling approach to many-body localization

Abstract

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 $\beta (g)=\mathrm{d}\log g/\mathrm{d}\log \mathrm{L}$ 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.

5 pages, 4 figures

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Cited by in corpus (6)

• Many-body localization transition in a lattice model of interacting fermions: statistics of renormalized hoppings in configuration space
• Do metals exist in two dimensions? A study of many-body localisation in low density electron gas
• The competition between antiferromagnetism and superconductivity in a doped Hubbard model with anisotropic interaction
• Non-Gaussian Spatial Correlations Dramatically Weaken Localization
• Universal Scaling of the Quantum Conductance of an Inversion-Symmetric Interacting Model
• Statistical properties of two-particle transmission at Anderson transition