Mailman 3 August 2021 - Kwant-discuss

Convergence of default solver near resonances
by dreitz＠physics.ucla.edu 31 Aug '21

31 Aug '21

Hello all, In follow-up to a recent question "Numerical precision of smatrix" https://mail.python.org/archives/list/kwant-discuss@python.org/thread/LZ22X… , I am also having issues with numerical precision and/or convergence of the wave functions inside the scattering region when using the default solver. Specifically, I am calculating tunnel couplings from a lead to a well through a barrier. There are resonances in the density of states at the energies of bound states inside the well, whose linewidth depends on the barrier height. When the resonances become too sharp, the DOS computed by Kwant becomes choppy and loses its well defined resonance characteristics. How can I improve the tolerance/precision of this calculation? The code to compute the DOS would look like this: wfs = kwant.wave_function(sys,energy=energy); wf = wfs(leadNum)[leadBandNum] rho = kwant.operator.Density(sys); density = rho(wf); Thanks, Derek

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Inquiry of applying Bound State Algorithm on 3D Systems
by Tiew, Hoe R 23 Aug '21

23 Aug '21

Good morning, We are writing this email as we would like to ask about the application of the bound state algorithm (described in https://scipost.org/10.21468/SciPostPhys.4.5.026) to higher-dimensional systems. In particular, we are trying to apply the algorithm to solve for proximitised 3DTIs, and for reference have been trying to understand the example cases of the quantum billiards and 2D topological insulator in the paper. Essentially, we would like to clarify if the reduction of higher-dimensional systems to quasi-1D is necessary for the bound state algorithm to work correctly. To solve for the 2D BHZ model (Section 5.2), the system was reduced to a quasi-1D system through the use of the Bloch theorem, and was then fed into the bound state algorithm. In section 4 however, a system of quantum billiards was considered without any mention of reduction to a quasi-1D system. As we are trying to apply the algorithm to a 3D system, we are wondering if this is a necessary step for the algorithm to work as intended. In the proximitised 3DTI systems we are considering, the leads are translationally invariant only in 1 direction, so we are wondering if the algorithm can be applied if we do need to reduce the system like in section 5.2. Thank you very much! Regards, Ryan and Chi

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kwant much faster in conda?
by Gerson J. Ferreira 20 Aug '21

20 Aug '21

Hello everyone, This might be a bit off topic. I've been using kwant via anaconda for a while because it was easier to install, but recently I've moved to a standard virtualenv and compiled kwant on my own (including mumps and openblas). But I've notice that my code is running much faster in conda+kwant than in my virtualenv+kwant. I'm still tracking why is there such a huge difference. The code basically builds a system without leads, extract the "hamiltonian_submatrix" for a given set of parameters and calculates the eigenvalues. Then I loop over a set of parameters. Running the code in the conda environment, it takes 15 minutes, but in my own virtualenv with compiled kwant it takes 2 hours!! It's exactly the same code. In conda the numpy runs with MKL, while in my virtualenv it runs with openblas. I've run a benchmark and the MKL is giving a near 2x speedup over OpenBlas for SVD and eigenvalues. I've compiled kwant with MUMPS and it seems ok. I've also tested with the kwant binary from Debian packages by setting "include-system-site-packages = false" and it get the same result (2h running time). Is there anything else I could be missing that would speed up the code? It seems that numpy is not the problem, since the MKL vs OpenBlas is at most a factor of 2. Maybe my compilation is not properly linking to MUMPS? How can I check if my kwant compilation is properly using openblas and MUMPS?

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Getting the List of Neighbors After finalization
by Henry Axt 19 Aug '21

19 Aug '21

I am attempting to approximate the first derivate over the system's wavefunction values, yet it seems there is no neighbors() function to call after finalization of the system. What would be the method to attain a list of neighboring sites after finalizaion? Is the ordering of the sites preserved before and after finalization?

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Units
by Jalil Varela 18 Aug '21

18 Aug '21

Hello, I'm a new kwant user, and i'm trying to reproduce some papers using real units and surges me a lot of questions regarding the internal units in kwant, if anyone understands, could you give me an idea? Usually the examples in kwant are chosen such that the units are given by (t=a=1), where (t) naturally depends on the value of (a) by means of t=hbar**2/(2ma**2), using this fact then the matrix elements of the hamiltonian are commonly defined , this parameters enter in the hamiltonian by means of the building of the lattice: lat = kwant.lattice.square(a=a, norbs=norbs) the matrix elements of the hamiltonian(e.g. with Rashba SOC): sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = -t * sigma_0 - 1j * alpha * sigma_y and from now on, all the calculations are given in terms of this units: for example, the energy units are in terms of [t] , the time unit are in (hbar/[t]), and the unit of distance in terms of [a], this means that for example 1 step in kwant energy correspond to one step of t in whatever units it has, is this correct? or am I missing something? Then assuming that i give the following values t=0.1 #in what units? can I simply assume that are eV? and for whatever reason i choose a=1 in this case what unit correspond to a?, I suppose that it has a unit such that t=hbar**2/(2ma**2)=0.1#in eV? Is this correct? and again once I replace this value in kwant, then the unit of energy is given by 0.1 eV, that is in steps of t, or in eV? How the system recognize in what units i want to work? If you have more comments about the units of the operators this will help me a lot, for example I understand that the units of of the observable are the same that the explicit formulas that appears in the tkwant review? for example the wave density has units of 1/sqrt(E), according to normalization formula and furthermore the current has no units, is this correct? again thank you and sorry for the stupid questions!

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Units
by Jalil Varela 17 Aug '21

17 Aug '21

Hello, I'm a new kwant user, and i'm trying to reproduce some papers using real units and surges me a lot of questions regarding the internal units in kwant, if anyone understands, could you give me an idea? Usually the examples in kwant are chosen such that the units are given by (t=a=1), where (t) naturally depends on the value of (a) by means of t=hbar**2/(2ma**2), using this fact then the matrix elements of the hamiltonian are commonly defined , this parameters enter in the hamiltonian by means of the building of the lattice: lat = kwant.lattice.square(a=a, norbs=norbs) the matrix elements of the hamiltonian(e.g. with Rashba SOC): sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = -t * sigma_0 - 1j * alpha * sigma_y and from now on, all the calculations are given in terms of this units: for example, the energy units are in terms of [t] , the time unit are in (hbar/[t]), and the unit of distance in terms of [a], this means that for example 1 step in kwant energy correspond to one step of t in whatever units it has, is this correct? or am I missing something? Then assuming that i give the following values t=0.1 #in what units? can I simply assume that are eV? and for whatever reason i choose a=1 in this case what unit correspond to a?, I suppose that it has a unit such that t=hbar**2/(2ma**2)=0.1#in eV? Is this correct? and again once I replace this value in kwant, then the unit of energy is given by 0.1 eV, that is in steps of t, or in eV? How the system recognize in what units i want to work? If you have more comments about the units of the operators this will help me a lot, for example I understand that the units of of the observable are the same that the explicit formulas that appears in the tkwant review? for example the wave density has units of 1/sqrt(E), according to normalization formula and furthermore the current has no units, is this correct? again thank you and sorry for the stupid questions!

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conservation_law in the case of sub-lattices with different numbers of orbitals
by Adel Belayadi 16 Aug '21

16 Aug '21

Dear Kwant user, Good day and I hope this email finds you well. Using conservation law was fully explained, in the Kwant mailing list, while we are having sublattices with the same degree of freedom (same number of orbitals). For instance, if we have two sites with *3 orbitals* in the case of a spin full Hamiltonian, the onsite matrix is (onsite_matrix( *6*6*) for each site ). So in this case, the conservation law will be straightforward: *conservation_law=-np.kron(**sigma_z, np.eye(3))*.*But what would be the case if we are dealing with sublattices which have different numbers of orbitals?* In my case, I am interested in spin conductance. I am using 3 sublattices with different orbitals. Let us say for instance sublattice0 has (*6-orbitals*), sublattice1 with (*2-orbitals*) and sublattice2 with (*2-orbitals*). In fact I am working on hetero-structure with two sites of C-like(pz with spin up and down) and one site of metal-like(3d-orbitals with spin up and down). I can resume my lattice as follow lat = kwant.lattice.general(prim_vecs, basis=[ [...], [...], [...]] , norbs=[6, 2, 2]) metal-like_sub, C-like_sub1, C-like_sub2 = lat.sublattices According to my understanding the conservation law would be something like conservation_law=-np.kron(sigma_z, np.eye(5))*. *However Kwant raises an error with my choice of the conservation law. Is there something missing with my understanding of the conservation law!. Or in the case of different orbitals per site, we need to define two lattices (lattice1 for spin up and lattice2 for spindown). Thanks in advance, Best

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Numerical precision of smatrix
by Jannis Neuhaus-Steinmetz 15 Aug '21

15 Aug '21

Dear all, I am having problems, that might be caused by the numerical precision of the smatrix solvers. I use the sign of the determinant of the reflection matrix [1] for the topological classification of my system. I calculate the reflection matrix with smatrix = kwant.solvers.default.smatrix(syst, energy=0.0, params=params, out_leads=[0], in_leads=[0]) In some cases the returned determinant is close to zero, but with the wrong sign. I am sure, that the sign is wrong, because it is sometimes -1, when the system is definitely not topological. In these cases, the sign changes to +1 when the parameters only slightly change (+-0.005 t). The code also works well for the most parts of the parameter space, i.e. everywhere where the absolute value of the determinant is not small. Is there any way to increase the precision of smatrix? It might just be the result of some rounding / float precision. Thanks, Jannis [1] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.057001

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