Can Kwant calculate density of states of quasi onedimensional systems?
Dear Kwant users,
In Kwant manual there is a section entitled "Calculating spectral density with the kernel polynomial method". I find that examples in this section are all talking about finitesize systems. I wonder whether Kwant can calculate density of states of a quasi onedimensional system that is finite along ydirection but is translationally invariant along xdirection. For a minimal test, I have run the following codes but errors occurred. # import kwant import numpy
a=1 W=30 t=1 lat = kwant.lattice.square(a) syst = kwant.Builder(kwant.TranslationalSymmetry((a, 0))) syst[(lat(0, j) for j in range(W))] = 4 * t syst[lat.neighbors()] = t fsyst = syst.finalized() energies = numpy.linspace(0.1,0.1, 10)
spectrum = kwant.kpm.SpectralDensity(fsyst) spectrum.add_moments(10) spectrum.add_vectors(5) densities = spectrum(energies)
# What's wrong in above codes? Currently, are we able to employ Kwant to calculate density of states of 3D systems being translationally invariant along one or two directions?
Regards, Zhan
Hi Zhan,
SpectralDensity indeed doesn't support translationally invariant systems. You have two options instead. If you want to obtain the DOS at a specific energy, you should use the output of syst.modes—specifically the wave functions of the propagating modes. If you need the DOS of the full spectrum, you should diagonalize the Hamitlonian and perform a summation over all momenta on your own.
Best, Anton
On Sat, 21 Dec 2019 at 13:51, Cao Zhan caozhan@baqis.ac.cn wrote:
Dear Kwant users,
In Kwant manual there is a section entitled "Calculating spectral density with the kernel polynomial method". I find that examples in this section are all talking about finitesize systems. I wonder whether Kwant can calculate density of states of a quasi onedimensional system that is finite along ydirection but is translationally invariant along xdirection. For a minimal test, I have run the following codes but errors occurred. # import kwant import numpy
a=1 W=30 t=1 lat = kwant.lattice.square(a) syst = kwant.Builder(kwant.TranslationalSymmetry((a, 0))) syst[(lat(0, j) for j in range(W))] = 4 * t syst[lat.neighbors()] = t fsyst = syst.finalized() energies = numpy.linspace(0.1,0.1, 10)
spectrum = kwant.kpm.SpectralDensity(fsyst) spectrum.add_moments(10) spectrum.add_vectors(5) densities = spectrum(energies) # What's wrong in above codes? Currently, are we able to employ Kwant to calculate density of states of 3D systems being translationally invariant along one or two directions?
Regards, Zhan
Hi Anton,
Thanks for your two suggestions. I am able to perform the second method but I don't know how to call syst.modes. Would you please show me the codes using syst.modes to calculate DOS(energy=0) of my minimal example? # import kwant import numpy
a=1 W=30 t=1 lat = kwant.lattice.square(a) syst = kwant.Builder(kwant.TranslationalSymmetry((a, 0))) syst[(lat(0, j) for j in range(W))] = 4 * t syst[lat.neighbors()] = t fsyst = syst.finalized()
# Then how to use fsyst.modes to calculate DOS(energy=0) ? #
Thanks in advance!
Regards, Zhan
发件人：Anton Akhmerov anton.akhmerov+kd@gmail.com 发送日期：20191221 21:55:34 收件人：Cao Zhan caozhan@baqis.ac.cn 抄送人：kwantdiscuss kwantdiscuss@kwantproject.org 主题：Re: [Kwant] Can Kwant calculate density of states of quasi onedimensional systems?>Hi Zhan,
SpectralDensity indeed doesn't support translationally invariant systems. You have two options instead. If you want to obtain the DOS at a specific energy, you should use the output of syst.modes—specifically the wave functions of the propagating modes. If you need the DOS of the full spectrum, you should diagonalize the Hamitlonian and perform a summation over all momenta on your own.
Best, Anton
On Sat, 21 Dec 2019 at 13:51, Cao Zhan caozhan@baqis.ac.cn wrote:
Dear Kwant users,
In Kwant manual there is a section entitled "Calculating spectral density with the kernel polynomial method". I find that examples in this section are all talking about finitesize systems. I wonder whether Kwant can calculate density of states of a quasi onedimensional system that is finite along ydirection but is translationally invariant along xdirection. For a minimal test, I have run the following codes but errors occurred. # import kwant import numpy
a=1 W=30 t=1 lat = kwant.lattice.square(a) syst = kwant.Builder(kwant.TranslationalSymmetry((a, 0))) syst[(lat(0, j) for j in range(W))] = 4 * t syst[lat.neighbors()] = t fsyst = syst.finalized() energies = numpy.linspace(0.1,0.1, 10)
spectrum = kwant.kpm.SpectralDensity(fsyst) spectrum.add_moments(10) spectrum.add_vectors(5) densities = spectrum(energies) # What's wrong in above codes? Currently, are we able to employ Kwant to calculate density of states of 3D systems being translationally invariant along one or two directions?
Regards, Zhan
participants (2)

Anton Akhmerov

Cao Zhan