Re: [Kwant] [KWANT] Diagonalization of hamiltonian
Thank you so much for your time. I will try it. Naveen Department of Physics & Astrophysics University of Delhi New Delhi-110007 On Mon, Apr 29, 2019, 16:32 Joseph Weston wrote: > > > > > I have build the system(discretized in x and y direction). The actual > > problem is that, " How to add magnetic field term(as given by the > > auther l_m = 4.5) to this system?" These bands are in presence of > > magnetic field. > > > Well you'll have to look in the paper to answer that question; you're in > a better position to answer that than me. Maybe a Peierls phase? > > >
Re: [Kwant] [KWANT] Diagonalization of hamiltonian
> > I have build the system(discretized in x and y direction). The actual > problem is that, " How to add magnetic field term(as given by the > auther l_m = 4.5) to this system?" These bands are in presence of > magnetic field. Well you'll have to look in the paper to answer that question; you're in a better position to answer that than me. Maybe a Peierls phase? signature.asc Description: OpenPGP digital signature
Re: [Kwant] [KWANT] Diagonalization of hamiltonian
Dear Joe, I have build the system(discretized in x and y direction). The actual problem is that, " How to add magnetic field term(as given by the auther l_m = 4.5) to this system?" These bands are in presence of magnetic field. Naveen Department of Physics & Astrophysics University of Delhi New Delhi-110007 On Mon, Apr 29, 2019, 15:20 Joseph Weston wrote: > Hi, > > > Dear Joe, > I just want to plot the Landau levels of the edge states without taking > into account the spin of particle for the thin slab with Wx =10 and Wy = > 50. Here Wx and Wy are the width of slab in x and y direction and magnetic > field is along x direction. And kz is a continuous function of Energy. > For more detail to this context, please take a look at the attached pdf > fig. (7) > > > >> > I want to diagonalize the model hamiltonian containing sine and cosine >> > functions with momentum operators as their argument. >> > >> > H(k) = tx*σx* sin kx + ty*σy*sin ky + mk*σz + λ*σ0 *sin kz, >> > >> > mk = tz(cos β − cos kz) + t'(2 − cos kx − cos ky) > > > So what you actually want to do is discretize this Hamiltonian in the x > and y directions, and then diagonalize the discretized Hamiltonian as a > function of the remaining k_z parameter. > > You can discretize this Hamiltonian by identifying the different terms > with onsites and hoppings. Start by writing the terms involving kx and ky > as exponentials, then factor out the terms multiplying exp(ikx) and > exp(iky) (and their Hermitian conjugates), and the remaining terms (with no > exponential). The onsite for your discretized model is the sum of terms > with no exponential, hopping in x direction is the term multiplying > exp(ikx) and hopping in y direction is the term multiplying exp(iky). > > At a glance it seems that you will end up with an onsite that depends on > kz, and that the hoppings will be independent of kz. > > Then once you've identified the onsite and hopping terms, use Kwant to > make a finite slab with the onsites and hoppings you derived, then get the > Hamiltonian as a function of kz using 'syst.hamiltonian_submatrix' and > diagonalize it to get the bands. > > Hope that helps. > > Happy Kwanting, > > Joe >
Re: [Kwant] [KWANT] Diagonalization of hamiltonian
Hi, > Dear Joe, > I just want to plot the Landau levels of the edge states without > taking into account the spin of particle for the thin slab with Wx =10 > and Wy = 50. Here Wx and Wy are the width of slab in x and y direction > and magnetic field is along x direction. And kz is a continuous > function of Energy. > For more detail to this context, please take a look at the attached > pdf fig. (7) > > > > > I want to diagonalize the model hamiltonian containing sine and > cosine > > functions with momentum operators as their argument. > > > > H(k) = tx*σx* sin kx + ty*σy*sin ky + mk*σz + λ*σ0 *sin kz, > > > > mk = tz(cos β − cos kz) + t'(2 − cos kx − cos ky) > So what you actually want to do is discretize this Hamiltonian in the x and y directions, and then diagonalize the discretized Hamiltonian as a function of the remaining k_z parameter. You can discretize this Hamiltonian by identifying the different terms with onsites and hoppings. Start by writing the terms involving kx and ky as exponentials, then factor out the terms multiplying exp(ikx) and exp(iky) (and their Hermitian conjugates), and the remaining terms (with no exponential). The onsite for your discretized model is the sum of terms with no exponential, hopping in x direction is the term multiplying exp(ikx) and hopping in y direction is the term multiplying exp(iky). At a glance it seems that you will end up with an onsite that depends on kz, and that the hoppings will be independent of kz. Then once you've identified the onsite and hopping terms, use Kwant to make a finite slab with the onsites and hoppings you derived, then get the Hamiltonian as a function of kz using 'syst.hamiltonian_submatrix' and diagonalize it to get the bands. Hope that helps. Happy Kwanting, Joe signature.asc Description: OpenPGP digital signature
Re: [Kwant] [KWANT] Diagonalization of hamiltonian
Hi, > I want to diagonalize the model hamiltonian containing sine and cosine > functions with momentum operators as their argument. > > H(k) = tx*σx* sin kx + ty*σy*sin ky + mk*σz + λ*σ0 *sin kz, > > mk = tz(cos β − cos kz) + t'(2 − cos kx − cos ky) If you just want to diagonalize a 2x2 H(k) then you don't even need Kwant; you can just make a function that gives you H(k) given a k vector, and then diagonalize the result using scipy.linalg.eigs. > Then I want to plot the energy dispersion as a function of kz in the > presence of perpendicular magnetic field. Here perpendicular direction > is x. Does the model already contain the terms for a magnetic field in the x direction? The answer will depend on what effects you are taking into account: do you want the orbital component, or just the action on the spin degree of freedom? The answer will depend on what you are trying to model, and this is a question that you will need to answer for yourself. Happy Kwanting, Joe signature.asc Description: OpenPGP digital signature
[Kwant] [KWANT] Diagonalization of hamiltonian
Dear KWANT developers, I want to diagonalize the model hamiltonian containing sine and cosine functions with momentum operators as their argument. H(k) = tx*σx* sin kx + ty*σy*sin ky + mk*σz + λ*σ0 *sin kz, mk = tz(cos β − cos kz) + t'(2 − cos kx − cos ky) Then I want to plot the energy dispersion as a function of kz in the presence of perpendicular magnetic field. Here perpendicular direction is x. Could anybody suggest me how to do this using kwant? I am new to kwant. Thanks in advance. Best,Naveen Naveen Department of Physics & Astrophysics University of Delhi New Delhi-110007
