diff --git a/docs/index.md b/docs/index.md index 32023a9..b439ad1 100644 --- a/docs/index.md +++ b/docs/index.md @@ -230,12 +230,14 @@ Source: Haldane, F. D. M. (1988). Model for a quantum Hall effect without Landau We denote $\{\mathbf{a}_i\}$ are the vectors from a B site to its three nearest-neighbor A sites, and $\{\mathbf{b}_i\}$ are next-nearest-neighbor distance vectors, then we have $$ -{\mathbf{a}_1} = (0,a),\\ -{\mathbf{a}_2} = (\sqrt 3 a/2, - a/2),\\ -{\mathbf{a}_3} = ( - \sqrt 3 a/2, - a/2)\\ -{\mathbf{b}_1} = {\mathbf{a}_2} - {\mathbf{a}_3} = (\sqrt 3 a,0),\\ -{\mathbf{b}_2} = {\mathbf{a}_3} - {\mathbf{a}_1} = ( - \sqrt 3 a/2, - 3a/2),\\ -{\mathbf{b}_3} = {\mathbf{a}_1} - {\mathbf{a}_2} = ( - \sqrt 3 a/2,3a/2) +\begin{aligned} +{\mathbf{a}_1} &= (0,a),\\ +{\mathbf{a}_2} &= (\sqrt 3 a/2, - a/2),\\ +{\mathbf{a}_3} &= ( - \sqrt 3 a/2, - a/2)\\ +{\mathbf{b}_1} &= {\mathbf{a}_2} - {\mathbf{a}_3} = (\sqrt 3 a,0),\\ +{\mathbf{b}_2} &= {\mathbf{a}_3} - {\mathbf{a}_1} = ( - \sqrt 3 a/2, - 3a/2),\\ +{\mathbf{b}_3} &= {\mathbf{a}_1} - {\mathbf{a}_2} = ( - \sqrt 3 a/2,3a/2) +\end{aligned} $$ Then the Haldane model on a hexagonal lattice can be written as