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) \(\propto\) 1/k α, 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 m for a finite system, and has perfect finite-size scaling behaviors around α m . It indicates that the first-order derivative of the spectrum-averaged von Neumann entropy has singular behavior, and α m can be used as a signature for transition points. For the infinite system, the threshold value α c = 1.465 is obtained by extrapolating α m .
KeywordsSystem Size Scaling Behavior Singular Behavior Amico Energy Level Statistic
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- 13.See, for example, The Physics of Quantum Information, edited by D. Bouwmeester, A. Ekert, A. Zeilinger (Springer, Berlin, 2000) Google Scholar
- 28.In practice, εβ is the average values over a small window Δ around an energy value E, i.e., Eβ ∈ [E-Δ/2, E+Δ/2]. We ensure that Δ is sufficiently small, and at the same time there are enough states in the interval Δ. Here Δ = 0.04 is chosen and other Δ give similar results Google Scholar