von Neumann entropy signatures of a transition in one-dimensional electron systems with long-range correlated disorder

We study the von Neumann entropy and related quantities in one-dimensional electron systems with on-site long-range correlated potentials. The potentials are characterized by a power-law power spectrum S(k) <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\propto$</EquationSource> </InlineEquation> 1/k <Superscript>α</Superscript>, where α is the correlation exponent. We find that the first-order derivative of spectrum-averaged von Neumann entropy is maximal at a certain correlation exponent α <Subscript> m </Subscript> for a finite system, and has perfect finite-size scaling behaviors around α <Subscript> m </Subscript>. It indicates that the first-order derivative of the spectrum-averaged von Neumann entropy has singular behavior, and α <Subscript> m </Subscript> can be used as a signature for transition points. For the infinite system, the threshold value α <Subscript> c </Subscript>=1.465 is obtained by extrapolating α <Subscript> m </Subscript>. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010