Mailman 3 September 2023 - Kwant-discuss

Package announcement: Pymablock
by Anton Akhmerov 12 Nov '23

12 Nov '23

Hello fellow Kwanters, I am happy to announce Pymablock, a Python package useful to combine with Kwant. Its main purpose is constructing effective models using perturbation theory, which may help you in different ways. Pymablock allows you to analyse the behavior of a few levels of a large Hamiltonian, or to construct a symbolic k.p model. We originally wrote the code for one of our projects, but then saw that this tool is useful almost for the entire group, so we decided to turn it into a package. We spent countless hours generalizing, optimizing, and testing it so that it is efficient and reliable. Now it handles multiple perturbations to any order, and it is compatible with symbolic and numerical calculations. We hope that Pymablock will save you a lot of effort and computation time. To see where it can help, check out our its documentation (https://pymablock.rtfd.io/), and in particular the tutorials about the k.p model of bilayer graphene (https://pymablock.readthedocs.io/en/latest/tutorial/bilayer_graphene.html) or the induced superconducting gap (https://pymablock.readthedocs.io/en/latest/tutorial/induced_gap.html). Just like Kwant, Pymablock is open source (https://gitlab.kwant-project.org/qt/pymablock), and you are welcome to follow and contribute to its development. Let us know if you have any questions or comments! Also if there's interest we can organize an online introduction of the package Best, Anton Akhmerov and the Pymablock maintainers: Isidora Araya Day and Sebastian Miles

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Realistic values of hopping parameters
by Yu Li 18 Oct '23

18 Oct '23

Dear all, Now I’m studying some transport property based on multilayered system, with nonmagnetic layer/ferromagnetic layer (NM/FM) stack. May I ask when creating a tight binding system, and setting hoppings by the following function: syst[(lat(1, 0), lat(1, 1))] = t, how to associate the hopping with a realistic system? Such as hoppings between FM and FM atoms, or between FM and NM atoms? I found in many literatures people just simply put t=1, but I assume the value should depend on the type of atoms. My another question is, is it possible to define more than one type of hopping between two sites? For the tight-binding approximation of p electrons, there are two types of hopping integrals: Vppσ, and Vppπ, so I’m wondering if it’s possible to simulate the effect of both hoppings? Thanks a lot for reading my questions! Cheers, Yu Li

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Hubbard model and self-consistent procedure
by 郭宇飞 28 Sep '23

28 Sep '23

Dear Kwant developers and users, Thank you for your contributions to the great software. I am trying to reproduce the result demonstrated in Figure 7(a) https://journals.aps.org/prb/abstract/10.1103/PhysRevB.79.205430 The model includes hopping term t and Hubbard potential U in a hexagonal lattice. I did the self-consistent process by Kwant to calculate the spin density distribution of the system. But the results seem to be incorrect on the distribution of spin density. I attached my code: sys = my_sys().finalized() def Fermi(E, mu, T): return 1/(exp((E - mu)/T) + 1) def sorted_eigs(ev): evals,evecs=ev evals,evecs=map(np.array,zip(*sorted(zip(evals,evecs.transpose())))) return evals,evecs.transpose() def Hartree_Fock(Du,Dd,ncc=200): m=50 H=sys.hamiltonian_submatrix(sparse=True) for nc in range(ncc): H0=H D=list(itertools.chain(*zip(Du,Dd))) H1=np.diag(D) H2=H0+H1 evals,evecs=sorted_eigs(sla.eigsh(H2,k=m,sigma=0)) up=evecs[::2] down=evecs[1::2] fermi_up= Fermi(evals,mu, T).reshape(1,m) fermi_down= Fermi(evals,mu, T).reshape(1,m) Du=(up*up.conj()*fermi_up).sum(axis=1,dtype='double') Dd=(down*down.conj()*fermi_down).sum(axis=1,dtype='double') if nc%5==0: print(f"N_step {nc} Loop") return Du,Dd Du=0.5*np.ones(605) Dd=np.zeros(605) Du,Dd=Hartree_Fock(Du,Dd) Dz=Du-Dd Dv=Du+Dd kwant.plotter.density(sys,Dd,relwidth=0.02,colorbar=True) kwant.plotter.density(sys,Du,relwidth=0.02,colorbar=True) kwant.plotter.density(sys,Dz,relwidth=0.02,colorbar=True) kwant.plotter.density(sys,Dv,relwidth=0.02,colorbar=True) 1. In the above code I use sys.hamiltonian_submatrix in Kwant to calculate the Hamitonian of the system. This Hamiltonian is not only a scattering region but it might have lead part in it, so how do I distinguish the matrix elements in wires and scattering center? Is it would induce the error in my results? 2. Since I did not find the self-consistent process of Hubbard model in the kwant documentation, I set a loop to calculate the spin density distribution of the system and draw the spin density distribution with kwant.plotter.density in kwant, I am not sure whether this part is correct. Anyone can give some suggestions or comments to have a different method on this part? Thank you in advance for your kindly help, Best wishes, Yufei Guo

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PBC to OBC conversions on Hamiltonians
by Haxxx Akxxx 26 Sep '23

26 Sep '23

I have k_x k_y k_z dependent PBC hamiltonian(2x2). And I want to go from PBC to OBC by limiting size along y such as N_y=5 and have a resultant hamiltonian(10x10) PBC-OBC-PBC. In kwant can we do such things?

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Green’s Functions in Tkwant
by Gabriel Garcia 26 Sep '23

26 Sep '23

Hi devs, I have been reproducing section 2.7, “Green’s Functions”. In this section, the tutorial shows us how to calculate Green’s functions for a 1D monoatomic network with two impurities. We learn to calculate all different types of time-dependent and independent Green functions. However, I have a question. When we consider a stationary system, the Green functions will be calculated depending on the Energy of the system. In the impurities example, the Green functions were calculated by varying the onsite energy of the impurities. How can I calculate the Green functions in terms of the system’s energy? Remembering that stationary Green functions are integrals of the system’s energy. Best, Gabriel Garcia

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Issue with Tutorial Example
by Dibyendu Kuiri 24 Sep '23

24 Sep '23

Dear Tkwant Forum, I hope this message finds you well. I am writing to bring to your attention an issue I encountered while trying to follow the tutorial on Tkwant. I am using Ubuntu 22.04.3 LTS ." Unfortunately, the example provided in the tutorial does not seem to be functioning as expected in this environment. Here are the details of my system: Description: Ubuntu 22.04.3 LTS In [1]: import kwant In [2]: kwant.__version__ Out[2]: '1.4.4' In [3]: import tkwant In [4]: tkwant.__version__ Out[4]: '1.1.0' numpy.__version__)" 1.25.2 scipy.__version__)" 1.11.2 I am getting the error as "/home/dkuiri/Dropbox/Tkwant/1d_wire_onsite.py:53: RuntimeWarning: Kwant's plotting functions have the side effect of selecting the matplotlib backend. To avoid this warning, import matplotlib.pyplot, matplotlib.backends or call matplotlib.use(). kwant.plot(syst) capi_return is NULL Call-back cb_fcn_in___user__routines failed. Traceback (most recent call last): File "/home/dkuiri/Dropbox/Tkwant/1d_wire_onsite.py", line 88, in <module> main() File "/home/dkuiri/Dropbox/Tkwant/1d_wire_onsite.py", line 73, in main state.evolve(time) File "/opt/miniconda3/envs/python3/lib/python3.9/site-packages/tkwant/manybody.py", line 2134, in evolve self.manybody_wavefunction.evolve(time) File "/opt/miniconda3/envs/python3/lib/python3.9/site-packages/tkwant/manybody.py", line 973, in evolve onebody_psi.evolve(time) File "/opt/miniconda3/envs/python3/lib/python3.9/site-packages/tkwant/onebody/onebody.py", line 442, in evolve next_psibar = self.solver(self.psibar, self.time, time, File "tkwant/onebody/solvers.pyx", line 69, in tkwant.onebody.solvers.Scipy.__call__ File "/home/dkuiri/.local/lib/python3.9/site-packages/scipy/integrate/_ode.py", line 1174, in run x, y, iwork, istate = self.runner(*((f, t0, y0, t1) + File "tkwant/onebody/solvers.pyx", line 60, in tkwant.onebody.solvers.Scipy._rhs File "tkwant/onebody/kernels.pyx", line 983, in tkwant.onebody.kernels._CalcRHSc.__call__ File "tkwant/onebody/kernels.pyx", line 977, in tkwant.onebody.kernels._CalcRHSc.__call__ File "tkwant/onebody/kernels.pyx", line 801, in tkwant.onebody.kernels.PerturbationInterpolator.apply File "tkwant/onebody/kernels.pyx", line 769, in tkwant.onebody.kernels.PerturbationInterpolator.evaluate File "tkwant/onebody/kernels.pyx", line 361, in tkwant.onebody.kernels.Interpolation.eval File "tkwant/onebody/kernels.pyx", line 416, in tkwant.onebody.kernels.Interpolation._estimate_stepsize TypeError: Cannot convert 'complex' with non-zero imaginary component to 'double' (this most likely comes from the '**' operator; use 'cython.cpow(True)' to return 'nan' instead of a complex number)." The issue I am facing, is it related the specific version? I would greatly appreciate any guidance or suggestions you can provide to help me resolve this issue and successfully complete the tutorial. Thank you for your assistance. Many thanks, Dibyendu Kuiri, Academic Centre for Materials and Nanotechnology AGH University of Science and Technology. Av. Mickiewicza 30 30-059 Krakow, Poland. email: kuiri(a)agh.edu.pl Phone no: +48 881293791 www.acmin.agh.edu.pl

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(no subject)
by jorge huamani 20 Sep '23

20 Sep '23

Dear all, My name is Jorge, the reason that I am sending this message is because I am new using tkwant, I am trying to use MPI to run my code, but I have issues when I want to run the average current (np.mean). I used to run parallel with the common way mpirun -n 40 python code.py. To run the current again time is not problem, but when I want to run and plot the current mean against voltage, unfortunately, the issue appears. I put here the photo of the loop that I am doing and the error that appears. By the last, I am following this paper PHYSICAL REVIEW B 93, 134506 (2016) [image: image.png] [image: image.png] Thank you so much for your help, -- Dr. Jorge Huamaní Correa Professor at Universidad Tecnológica del Perú CTI Vitae : https://ctivitae.concytec.gob.pe/appDirectorioCTI/VerDatosInvestigador.do?i…

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number of vectors for kpm.conductivity
by Sergey Slizovskiy 18 Sep '23

18 Sep '23

Dear Kwant Developers, Just a brief question: the memory in kpm conductivity calculation seem to scale as (system orbitals)*(moments)^2 * vectors . Pablo Piskunow has explained about moments^2 in the current implementation, the question is now about vectors. Can I run many calculations with num_vectors = 1 and then average the result? If yes, then I do not understand why the memory in the kwant implementation scales linearly with vectors: it seems that there is only one Trace in the formula, so, equivalent to averaging over vectors which is a linear in time operation, but not in memory. Thank you, Sergey

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Questions about kwant: the number of iterations
by meimeiwu＠buaa.edu.cn 05 Sep '23

05 Sep '23

Hi devs, I am learning kwant alone, but I have doubts. I have several confusions which are related to calculate transport by using kwant： 1. When disorder is included what the number of iterations or what is the convergence standard in calculation ？ 2. Will the length of scattering region affect computed result ？For example, I construct the system with scattering region and two leads, will the length of scattering region affect the transport properties? If the length of scattering region is too small, is there any interaction between two leads? If transport properties depend on the length of scattering region, what we should consider it? What calculations can illustrate the influence of the length of scattering region? what is the best solution or if you can give me some advices to solve that problem I will appreciate it, thanks a lot! Best regards

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On the numerical implementation of KPM for Kubo-Bastin formula
by bishihao＠connect.hku.hk 03 Sep '23

03 Sep '23

Dear All, Recently, I have been engaged in coding the kernel polynomial method for the Kubo-Bastin formula with the aim of investigating potential extensions, including GPU or FFT acceleration. As a concrete example, I have chosen the QWZ model, the 2D massive Dirac fermion, to calculate its Hall conductivity. In the stochastic approach, the conventional trace operation is substituted with an expectation value computed over a random phase vector. By leveraging the recursive relation of Chebyshev polynomials, the problem can be simplified to the computation of the inner product of a series of vectors, as depicted in kwant.kpm<https://kwant-project.org/doc/1/reference/kwant.kpm>. Nevertheless, when implementing the code using such a straightforward approach, the Hall conductivity exhibits significant fluctuations and fails to converge, even when increasing the system size, the number of random phase vectors, or the number of Chebyshev moments considered. In comparison, the Hall conductivity obtained from the kwant package demonstrates a robust behavior, exhibiting stability and consistent results in the band gap, as exhibits in the Appendix A. We observe that within the band gap, the Hall conductivity demonstrates perfect quantization. However, in the bulk region, an oscillatory behavior emerges as the number of Chebyshev moments increases. In an attempt to understand the underlying cause, I read the source code of kwant.kpm. A notable discovery was that instead of utilizing random phase vectors (although they are employed for calculating the density of states when vector_factory=None), the s_factory = kwant.kpm.LocalVectors(syst, where) function actually generates local vectors that represent a state at the center of the system. And it is similar for kwant.kpm.RandomVectors(syst, where). After implementing this modification in my own code, I observed that the Hall conductivity within the band gap became quantized, as expected. But the puzzle arises because, in the stochastic approach, the trace is obtained by averaging over random phase vectors, which is considered to be a complete sampling, and the self-average effect guarantees convergence. However, in the kwant.kpm implementation, a local state at the center of the disk in coordinate space is employed instead. The question then remains: why does this alternative approach yield accurate results? And why do the random phase vectors not yield valid results? Attached are my python codes. The FFT implementation I utilized is based on the reference arXiv:2307.09690<https://arxiv.org/abs/2307.09690>. Best wishes, Shihao * Appendix A: Kwant Code Attached is the Kwant code for calculating the Hall conductivity. I post it here in case the forum does not support attachments. [cid:5cb88c50-7d6c-4230-aa9d-189ed73c001d] [cid:e1e22a6b-a5f4-44dd-aac0-0b01c2796fd6] * Appendix B: FFT-accelerated Kubo-Bastin formula [cid:737ce999-435f-4f96-bf1e-4b065e239ce4] [cid:d1197b58-b4c9-4738-a5fc-4fda7979706f]

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