Metal-insulator transition in disordered systems from the one-body density matrix

Abstract

The insulating state of matter can be probed by means of a ground state geometrical marker, which is closely related to the modern theory of polarization (based on a Berry phase). In the present work we show that this marker can be applied to determine the metal-insulator transition in disordered systems. In particular, for non-interacting systems the geometrical marker can be obtained from the configurational average of the norm-squared one-body density matrix, which can be calculated within open as well as periodic boundary conditions. This is in sharp contrast to a classification based on the static conductivity, which is only sensible within periodic boundary conditions. We exemplify the method by considering a simple lattice model, known to have a metal-insulator transition as a function of the disorder strength and demonstrate that the transition point can be obtained accurately from the one-body density matrix. The approach has a general {\it ab-initio} formulation and can be applied to realistic disordered materials by standard electronic structure methods.

5 pages

References in corpus (3)

• Anderson Transitions
• Many-body localization characterized from a one-particle perspective
• Kohn's localisation in disordered fermionic systems with and without interactions

Cited by in corpus (4)

• Accurate ground state- and quasiparticle energies: beyond the RPA and GW methods with adiabatic exchange-correlation kernels
• Local theory of the insulating state
• Scaling and renormalization in the modern theory of polarization: application to disordered systems
• Mott-Anderson Metal-Insulator Transitions from Entanglement