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• W2075825574 abstract "Anderson orthogonality (AO) refers to the fact that the ground states of two Fermi seas that experience different local scattering potentials, say $|{G}_{mathrm{I}}ensuremath{rangle}$ and $|{G}_{mathrm{F}}ensuremath{rangle}$, become orthogonal in the thermodynamic limit of large particle number $N$, in that $|ensuremath{langle}{G}_{mathrm{I}}|{G}_{mathrm{F}}ensuremath{rangle}|ensuremath{sim}{N}^{ensuremath{-}frac{1}{2}{ensuremath{Delta}}_{mathrm{AO}}^{2}}$ for $Nensuremath{rightarrow}ensuremath{infty}$. We show that the numerical renormalization group offers a simple and precise way to calculate the exponent ${ensuremath{Delta}}_{mathrm{AO}}$: the overlap, calculated as a function of Wilson chain length $k$, decays exponentially $ensuremath{sim}{e}^{ensuremath{-}kensuremath{alpha}}$, and ${ensuremath{Delta}}_{mathrm{AO}}$ can be extracted directly from the exponent $ensuremath{alpha}$. The results for ${ensuremath{Delta}}_{mathrm{AO}}$ so obtained are consistent (with relative errors typically smaller than 1%) with two other related quantities that compare how ground-state properties change upon switching from $|{mathrm{G}}_{mathrm{I}}ensuremath{rangle}$ to $|{mathrm{G}}_{mathrm{F}}ensuremath{rangle}$: the difference in scattering phase shifts at the Fermi energy, and the displaced charge flowing in from infinity. We illustrate this for several nontrivial interacting models, including systems that exhibit population switching." @default.
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• W2075825574 date "2011-08-10" @default.
• W2075825574 modified "2023-09-23" @default.
• W2075825574 title "Anderson orthogonality and the numerical renormalization group" @default.
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• W2075825574 doi "https://doi.org/10.1103/physrevb.84.075137" @default.
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