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Erratum: Solution to the many-body problem in one point (New J. Phys. 16 113025)

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Published 28 November 2014 • © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft
, , Citation J A Berger et al 2014 New J. Phys. 16 119601 DOI 10.1088/1367-2630/16/11/119601

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This is a correction for 2014 New J. Phys. 16 113025

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  1. Received 14 November 2014
  2. Accepted 14 November 2014
  3. Published

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Due to a typesetting error, the following figures were not reproduced correctly. In addition, in the caption of figure 3, $u_{lin}^{0}/V$ should read $u_{lin}^{0}/v$

Figure 3.

Figure 3. The real part of the screened interaction in one point $u/v$ as a function of the interaction ${{[y_{0}^{0}]}^{2}}v$ ($\lambda =1$). Continuous line (black): $u_{lin}^{0}/v$; dashed line (red): ${{u}_{RPA}}/v$; double-dot-dashed line (orange): ${{u}_{GW}}/v$; dot-double-dashed line (violet): ${{u}_{GW\Gamma }}/v$; dotted line (green): exact solution. Inset (bottom-left corner): zoom for small ${{[y_{0}^{0}]}^{2}}v$. Inset (bottom-right corner): the imaginary part of $u/v$.

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Figure 4.

Figure 4. The real part of the screened interaction in one point $u/v$ as a function of the interaction ${{[y_{0}^{0}]}^{2}}v$ ($\lambda =\frac{1}{2}$). Continuous line (black): $u_{lin}^{0}/y_{0}^{0}$; dashed line (red): ${{u}_{RPA}}/v$; double-dot-dashed line (orange): ${{u}_{GW}}/v$; dot-double-dashed line (violet): ${{u}_{GW\Gamma }}/v$; dotted line (green): exact solution. Inset (top-left corner): zoom for small ${{[y_{0}^{0}]}^{2}}v$. Inset (bottom-left corner): the imaginary part of $u/v$.

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Figure 5.

Figure 5. The real part of the $GW$ Greenʼs function in one point as a function of the interaction ${{[y_{0}^{0}]}^{2}}v$ ($\lambda =1$). Continuous line (black): the physical solution ${{y}_{GW}}/y_{0}^{0}$; dashed line (red): the non-physical $GW$ solution ${{y}_{2}}/y_{0}^{0}$; dot-dashed line (blue): the non-physical $GW$ solution ${{y}_{3}}/y_{0}^{0}$; double-dot-dashed line (orange): the non-physical $GW$ solution ${{y}_{4}}/y_{0}^{0}$. Inset: the imaginary part of the $GW$ Greenʼs function.

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Figure 6.

Figure 6. The $GW$ Greenʼs function in one point as a function of the interaction ${{[y_{0}^{0}]}^{2}}v$ ($\lambda =1$). Continuous line (black): the physical solution ${{y}_{GW}}/y_{0}^{0}$; dashed line (red): the iterative $GW$ result (see main text for details); dotted line (blue): ${{y}_{{{G}^{0}}{{W}^{0}}}}/y_{0}^{0}$; dot-dashed line (green): ${{y}_{{{G}^{1}}{{W}^{1}}}}/y_{0}^{0}$. Inset: the screened interaction ${{u}_{GW}}/v$ as a function of the interaction ${{[y_{0}^{0}]}^{2}}v$.

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Figure 7.

Figure 7. The $GW$ Greenʼs function in one point as a function of the interaction ${{[y_{0}^{0}]}^{2}}v$ ($\lambda =\frac{1}{2}$). Continuous line (black): the physical solution ${{y}_{GW}}/y_{0}^{0}$; dashed line (red): the iterative $GW$ result (see main text for details); dotted line (blue): ${{y}_{{{G}^{0}}{{W}^{0}}}}/y_{0}^{0}$; dot-dashed line (green): ${{y}_{{{G}^{1}}{{W}^{1}}}}/y_{0}^{0}$. Inset: the screened interaction ${{u}_{GW}}/v$ as a function of the interaction ${{[y_{0}^{0}]}^{2}}v$.

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Figure 8.

Figure 8. The $GW\Gamma $ Greenʼs function in one point as a function of the interaction ${{[y_{0}^{0}]}^{2}}v$ ($\lambda =1$). Continuous line (black): the physical solution ${{y}_{GW\Gamma }}/y_{0}^{0}$; dashed line (red): the iterative $GW\Gamma $ result (see main text for details); dotted line (blue): ${{y}_{{{G}^{0}}{{W}^{0}}{{\Gamma }^{0}}}}/y_{0}^{0}$; dot-dashed line (green): ${{y}_{{{G}^{1}}{{W}^{1}}{{\Gamma }^{1}}}}/y_{0}^{0}$. Inset: the screened interaction ${{u}_{GW\Gamma }}/v$ as a function of the interaction ${{[y_{0}^{0}]}^{2}}v$.

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10.1088/1367-2630/16/11/119601