discretize continuous Hamiltonians
Dear authors, I want to discretize continuous Hamiltonians of Weyl semimetal (PRL 115,246603 (2015)) using Kwant, but we have sin(kz),sin(ky)...in the Hamiltonian, so it always shows the error message. I have already imported sin and cos from math. Could you give me any suggestion? Hosein Khani
Dear Khani, Kwant only discretizes Polynomials. However, the Hamiltonian you have can be implemented easily. Just think of writing the sin and cos functions as sum and difference of exponentials, and then take the factors as hoppings. Regards, Ousmane
Dear sir, Sorry to interrupt you, I have a query related to the discussion going here. Suppose if I have sin(2k_z) or cos(2k_z) term in the Hamiltonian which arises due to second neighbour hopping then how should I proceed? When I assign the factors which arise from these terms to the second neighbour hopping, I am getting wrong results. Best Regards On Fri, Aug 7, 2020, 22:06 <ousmane.ly@kaust.edu.sa> wrote:
Dear Khani, Kwant only discretizes Polynomials. However, the Hamiltonian you have can be implemented easily. Just think of writing the sin and cos functions as sum and difference of exponentials, and then take the factors as hoppings. Regards, Ousmane
Dear Naveen, In a square lattice for instance \exp(2 i\pm k.r) would rather correspond to a third nearest neighbor. This may be the reason of the discrepancy you observe. Regards, Ousmane
Dear sir, I am dealing with cubic lattice with first nearest neighbour hopping in all directions but second nearest neighbour hopping only in z-direction. Like *c_{j}^{/dagger} c_{j+2a/hat{z}} /sigma_0 + h.c*. So I get *cos(2k_z)* term in the Hamiltonian. If I expand this cosine term in polynomial form upto second order. The discretizer does not give any second neighbour hopping term like Hoppingkind(0,1, 1). The discretizer mix it with the first nearest neighbour hopping in z-direction. but If I write the cosine term like [exp(i2k_z)+exp(-i2k_z)]/2. So I have to assign 0.5 /sigma_0 to the Hoppingkind(0 1 1) and other similar type of second neighbour hoppings only in z direction. I am confused that which is the correct way to deal with this problem. I hope you understand what I mean. Thank you. Best Regards Naveen Yadav Research Scholar Department of Physics & Astrophysics University of Delhi New Delhi-110007 On Sat, Aug 8, 2020, 18:52 <ousmane.ly@kaust.edu.sa> wrote:
Dear Naveen, In a square lattice for instance \exp(2 i\pm k.r) would rather correspond to a third nearest neighbor. This may be the reason of the discrepancy you observe.
Regards, Ousmane
Hi Naveen, In fact, the Taylor expansion of the cos function up two second order doesn't contain more than the first nearest neighbor hopping, so the result doesn't correspond to the tight binding model you are comparing with. You should expand the function up to forth order, then you will be able to see second nearest neighbors from the kwant discretization. Regards, Ousmane
Dear sir, Thank you for the suggestion. I will try it. On Sat, Aug 8, 2020 at 11:46 PM <ousmane.ly@kaust.edu.sa> wrote:
Hi Naveen, In fact, the Taylor expansion of the cos function up two second order doesn't contain more than the first nearest neighbor hopping, so the result doesn't correspond to the tight binding model you are comparing with. You should expand the function up to forth order, then you will be able to see second nearest neighbors from the kwant discretization.
Regards, Ousmane
-- Best Regards, Naveen Yadav Research Scholar Department of Physics & Astrophysics University Of Delhi New Delhi-110007
Dear Khani, The function discretizing the continuous Hamiltonian works for a hamiltonian with a polynomial form in the variables kx, ky, kz, which is not the case in your Hamiltonian. What you can do is: 1) A Taylor expansion of your Hamiltonian, preferably to the second order. 2) Use the descritizing function of kwant with the Hamiltonian obtained by the expansion. (you can play with the order of the expansion too) 3) Check that it gives the form of your initial discretized Hamiltonian. This is not guaranteed to work all the time, but it is the fastest way in my opinion. I hope this helps, Adel On Fri, Aug 7, 2020 at 11:45 AM Khani Hosein <hoseinkhaniphy@gmail.com> wrote:
Dear authors, I want to discretize continuous Hamiltonians of Weyl semimetal (PRL 115,246603 (2015)) using Kwant, but we have sin(kz),sin(ky)...in the Hamiltonian, so it always shows the error message. I have already imported sin and cos from math. Could you give me any suggestion? Hosein Khani
-- Abbout Adel
Dear Adel, Thanks for your suggestion. I will try this to see if it works. Best regards Khani On Sat, Aug 8, 2020 at 6:42 AM Abbout Adel <abbout.adel@gmail.com> wrote:
Dear Khani,
The function discretizing the continuous Hamiltonian works for a hamiltonian with a polynomial form in the variables kx, ky, kz, which is not the case in your Hamiltonian.
What you can do is: 1) A Taylor expansion of your Hamiltonian, preferably to the second order. 2) Use the descritizing function of kwant with the Hamiltonian obtained by the expansion. (you can play with the order of the expansion too) 3) Check that it gives the form of your initial discretized Hamiltonian.
This is not guaranteed to work all the time, but it is the fastest way in my opinion.
I hope this helps, Adel
On Fri, Aug 7, 2020 at 11:45 AM Khani Hosein <hoseinkhaniphy@gmail.com> wrote:
Dear authors, I want to discretize continuous Hamiltonians of Weyl semimetal (PRL 115,246603 (2015)) using Kwant, but we have sin(kz),sin(ky)...in the Hamiltonian, so it always shows the error message. I have already imported sin and cos from math. Could you give me any suggestion? Hosein Khani
-- Abbout Adel
participants (4)
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Abbout Adel -
Khani Hosein -
Naveen Yadav -
ousmane.ly＠kaust.edu.sa