From 6d035013071124076b45ee63021e0d251f262acb Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Mon, 30 Nov 2020 11:24:27 +0100 Subject: [PATCH] RMP Hamiltonian for Hugh --- Manuscript/EPAWTFT.tex | 15 +++++++++++++-- 1 file changed, 13 insertions(+), 2 deletions(-) diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index e9983f8..4c8d55e 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -1272,10 +1272,21 @@ has a negative diagonal term in the one-electron Hamiltonian, representing the n encoded in the Initialisation section such that the core Hamiltonian is To model the doubly-occupied atom, we can define our reference HF state as the configuration with $\theta = 0$ and energy \begin{equation} - \frac{1}{2} (2 U - 4 \epsilon) + E_\text{HF}(0, 0) = \frac{1}{2} (2 U - 4 \epsilon) \end{equation} The RMP Hamiltonian then becomes -... +\begin{widetext} +\begin{equation} +\label{eq:H_RMP} +\bH_\text{RMP}\qty(\lambda) = + \begin{pmatrix} + -2 \delta \epsilon + 2U(1 - \lambda/2) & -\lambda t & -\lambda t & 0 \\ + -\lambda t & - \delta \epsilon + (1-\lambda)U & 0 & -\lambda t \\ + -\lambda t & 0 & - \delta \epsilon + (1-\lambda)U & -\lambda t \\ + 0 & -\lambda t & -\lambda t & \lambda U \\ + \end{pmatrix}, +\end{equation} +\end{widetext} } \hughDraft{%