Effect of Hilbert space truncation on Anderson localization

TL;DR

This paper investigates how truncating the Hilbert space in the 1-D Anderson model affects localization properties, eigenstate structure, and potential multifractal behavior, revealing impacts on Anderson localization phenomena.

Contribution

It introduces a study of Hilbert space truncation effects on Anderson localization, analyzing eigenstates and multifractality in a previously unexplored context.

Findings

Hilbert space truncation alters eigenstate localization.

Truncation influences multifractal characteristics.

Eigenstate measures show significant changes due to truncation.

Abstract

The 1-D Anderson model possesses a completely localized spectrum of eigenstates for all values of the disorder. We consider the effect of projecting the Hamiltonian to a truncated Hilbert space, destroying time reversal symmetry. We analyze the ensuing eigenstates using different measures such as inverse participation ratio and sample-averaged moments of the position operator. In addition, we examine amplitude fluctuations in detail to detect the possibility of multifractal behavior (characteristic of mobility edges) that may arise as a result of the truncation procedure.