Quantification of Correlations in Quantum Many-Particle Systems

We introduce a well-defined and unbiased measure of the strength of correlations in quantum many-particle systems which is based on the relative von Neumann entropy computed from the density operator of correlated and uncorrelated states. The usefulness of this general concept is demonstrated by quantifying correlations of interacting electrons in the Hubbard model and in a series of transition-metal oxides using dynamical mean-field theory.

Figure 1

Upper panel: Local von Neumann entropy of the correlated PM ground state as a function of the interaction $U$. Inset: double occupation in the PM (black curve) and the AFM (red curve) ground state compared to the Hartree-Fock result (green curve) as a function of $U$. Lower panel: local relative entropies (PM phase) between the correlated ground state and the noninteracting ($U=0$) and local moment ($U=\infty$) ground states, respectively, as functions of $U$.

Figure 2

Upper panel: local von Neumann entropy $S$ of the correlated AFM and the Slater ground states as a function of $U$. Lower panel: local relative entropies $\Delta S$ between correlated AFM, Slater, and Heisenberg ground states. $\Delta S(\widehat{\rho }\Vert {\widehat{\rho }}^{\mathrm{Slat}})$ and $\Delta S({\widehat{\rho }}^{\mathrm{Slat}}\Vert \widehat{\rho })$ are magnified by a factor of 50.

Figure 3

Left panels: local von Neumann (top) and relative (bottom) entropies for MnO, FeO, CoO, and NiO series. Right panels: local von Neumann (top) and relative (bottom) entropies for hole doped NiO; see text.