From 6ca70da81847a191b66224edac094c6b63d4ac48 Mon Sep 17 00:00:00 2001 From: Thibaut Lacroix <57836508+tfmlaX@users.noreply.github.com> Date: Wed, 15 May 2024 14:55:18 +0200 Subject: [PATCH] Fix a typo --- docs/src/examples/anderson-model.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/src/examples/anderson-model.md b/docs/src/examples/anderson-model.md index eebf18b..ed4c179 100644 --- a/docs/src/examples/anderson-model.md +++ b/docs/src/examples/anderson-model.md @@ -21,10 +21,10 @@ We remark that this is the same Bogoliubov transformation used in the thermofiel The thermofield-transformed Hamiltonian is then mapped on two chains, defined and constructed using the TEDOPA chain mapping: the chain labelled $1$ is for the empty modes, the chain labelled $2$ for the filled modes. The following relations are used to define the functions equivalent to the spectral density of the bosonic case, one for each chain: ```math -\begin{align} +\begin{aligned} &V_{1k} = V_{k} \sin \theta_k = \sqrt{\frac{1}{e^{\beta \epsilon_k}+1}} \\ &V_{2k} = V_{k} \cos \theta_k = \sqrt{\frac{1}{e^{-\beta \epsilon_k}+1}}, -\end{align} +\end{aligned} ``` where we choose the spectral function that characterizes the fermionic bath to be: $V_k= \sqrt{1-k^2}$, and we define the dispersion relation as: $e_k = k$, that is, a linear dispersion relation with propagation speed equal to $1$. This latter choice corresponds to a model of metals (gapless energy spectrum). We select a filled state as the initial state of the defect. Using the mapping proposed in [1], the chain Hamiltonian becomes: