Thanks a lot ! everything is clear and works fine.
Adel
On Mon, May 15, 2017 at 3:42 PM, Joseph Weston <joseph.westo...@gmail.com>
wrote:
> Hi,
>
> > Thank you Joseph for the highlight. It make sens since the tests on a
> > square lattice seemed working fine.
> >
> > I checked the 'plot_2d_bands' function but could not identify the
> > transformation you were mentioning. Could you help me in this please?
>
> It requires a bit of reading but we can extract the following snippets
> from 'wraparound' (I have reworded some comments to make sense without
> the surrounding context of the 'wraparound' module):
>
> # calculate the reciprocal symmetry vectors: these
> # are the columns of 'A'
> B = np.array(symmetry.periods).T
> A = B.dot(np.linalg.inv(B.T.dot(B)))
>
> ...
>
> # transforms a momentum in the basis (kx, ky) to the basis of
> # reciprocal symmetry vectors
> def momentum_to_lattice(k):
> k, residuals = scipy.linalg.lstsq(A, k)[:2]
> if np.any(abs(residuals) > 1e-7):
> raise RuntimeError("Requested momentum doesn't correspond"
> " to any lattice momentum.")
> return k
>
> We could then use 'momentum_to_lattice' like so:
>
> syst = make_wrapped_around_syst()
>
> H_k(kx, ky):
> k = (kx, ky)
> k_prime = momentum_to_lattice(k)
> return syst.hamiltonian_submatrix(args=k_prime)
>
> Does this help?
>
>
> > Just to check my understanding for this module, could you tell me if I am
> > right:
> > 1) one can plot the system sys (before wraping)
> > 2) check the extra-cell hoppings
> > 3) take them off and add terms of the form -t exp(i k .Vj) for the
> > corresponding intra-cell hopping (Vj is the vector of the eliminated
> > hopping)
> > with this, we obtain the Hamiltonian of the wrapped system
> >
> > am I correct ?
>
> Yes, in addition to the caveat that inter-cell hoppings between a site
> and its image under the symmetry will correspond to *onsite* terms in
> the wrapped around system (imagine a simple chain of sites with
> nearest-neighbor hoppings).
>
> Happy Kwanting,
>
> Joe
>
--
Abbout Adel
