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Triangular Lattice
Triangular Lattice
It would be useful to have an implementation for a triangular lattice integrated into the main code (tenpy.models.lattice), since it comes up so frequently. Many thanks ![Smile :)](./images/smilies/icon_e_smile.gif)
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Re: Triangular Lattice
Agreed.
The Triangular lattice is basically just a simple square lattice with one of the basis vectors rotated by 30 degrees towards the other. I'd suggest to use
If you quickly write down the (next-)(next-)nearest neighbors, I'll copy over the code from the tenpy.models.lattice.Square lattice and make the figure.
The Triangular lattice is basically just a simple square lattice with one of the basis vectors rotated by 30 degrees towards the other. I'd suggest to use
Code: Select all
basis = np.array([[0.5 *np.sqrt(3), 0.5], # first basis vector
[0., 1.]]) # second basis vector: y-direction
Re: Triangular Lattice
Using this basis, for a point at the origin:
There are 6 NN at a distance 1.
There are 6 nNN at a distance sqrt(3).
There are 6 nnNN at a distance 2.
Checked with Mathematica. Many thanks ![Smile :)](./images/smilies/icon_e_smile.gif)
There are 6 NN at a distance 1.
There are 6 nNN at a distance sqrt(3).
There are 6 nnNN at a distance 2.
Code: Select all
NN = {1/2 {Sqrt[3], 1}, {0, 1}, -(1/2) {Sqrt[3], 1}, -{0, 1}, 1/2 {Sqrt[3], -1}, 1/2 {-Sqrt[3], 1}};
nNN = {{Sqrt[3], 0}, {-Sqrt[3], 0}, 1/2 {Sqrt[3], 3}, -(1/2) {Sqrt[3], 3}, 1/2 {-Sqrt[3], 3}, 1/2 {Sqrt[3], -3}};
nnNN = {{0, 2}, {0, -2}, {Sqrt[3], 1}, -{Sqrt[3], 1}, {-Sqrt[3], 1}, {Sqrt[3], -1}};
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Re: Triangular Lattice
Implemented ![Wink ;)](./images/smilies/icon_e_wink.gif)
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