Onsite and hopping values in QHE
Hello everyone, I am trying to reproduce the QHE bar device calculations http://nbviewer.jupyter.org/github/topocm/topocm_content/blob/master/w3_pump... However, I am having difficulty with the onsite and hopping values as I am using TBModels https://github.com/Z2PackDev/TBmodels and therefore the values are not the same for all sites. The problem is that after the scalar values have been passed on to the Builder, these will then be overriden when using functions for the positiondependent Hamiltonian. I tried making a deep copy of the model, which would then serve as a data structure where to draw the scalar values from when calling the Onsite and Hopping functions. The problem with this is a) I am getting a KeyError which I am still not sure why it happens b) It does not feel very memoryefficient. I am wondering if there is another way that this could be done on the Kwant side that I have not been able to think of. Regards  Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz@auth.gr  tel:+30 2310 998109
HI,
I am trying to reproduce the QHE bar device calculations
http://nbviewer.jupyter.org/github/topocm/topocm_content/blob/master/w3_pump...
However, I am having difficulty with the onsite and hopping values as I am using TBModels
https://github.com/Z2PackDev/TBmodels
and therefore the values are not the same for all sites.
I am unsure of the output format of TBModels. Glancing at their documentation I can't see any way of getting the raw matrix elements from a "Model". Looking into the source code it seems that they are stored in a format that will be annoying to query manually.
The problem is that after the scalar values have been passed on to the Builder, these will then be overriden when using functions for the positiondependent Hamiltonian.
I tried making a deep copy of the model, which would then serve as a data structure where to draw the scalar values from when calling the Onsite and Hopping functions. The problem with this is
a) I am getting a KeyError which I am still not sure why it happens b) It does not feel very memoryefficient.
I am wondering if there is another way that this could be done on the Kwant side that I have not been able to think of.
I can't think of a better way to accomplish this. Using TBModels' internal datastructures directly is IMO too much hassle unless your systems are really big. Did you check that the symmetry of your Kwant system and the TBModels Model are compatible? Joe
Hello Joseph, Thank you. It is working when I copy the model and each lead after I have attached them. Regards, Eleni Quoting Joseph Weston <joseph.weston08@gmail.com>:
HI,
I am trying to reproduce the QHE bar device calculations
http://nbviewer.jupyter.org/github/topocm/topocm_content/blob/master/w3_pump...
However, I am having difficulty with the onsite and hopping values as I am using TBModels
https://github.com/Z2PackDev/TBmodels
and therefore the values are not the same for all sites.
I am unsure of the output format of TBModels. Glancing at their documentation I can't see any way of getting the raw matrix elements from a "Model". Looking into the source code it seems that they are stored in a format that will be annoying to query manually.
The problem is that after the scalar values have been passed on to the Builder, these will then be overriden when using functions for the positiondependent Hamiltonian.
I tried making a deep copy of the model, which would then serve as a data structure where to draw the scalar values from when calling the Onsite and Hopping functions. The problem with this is
a) I am getting a KeyError which I am still not sure why it happens b) It does not feel very memoryefficient.
I am wondering if there is another way that this could be done on the Kwant side that I have not been able to think of.
I can't think of a better way to accomplish this. Using TBModels' internal datastructures directly is IMO too much hassle unless your systems are really big.
Did you check that the symmetry of your Kwant system and the TBModels Model are compatible?
Joe
 Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz@auth.gr  tel:+30 2310 998109
Hello everyone, While this is working in a system with leads, I am getting an error in the case of a closed system.  sym = kwant.TranslationalSymmetry( lattice.vec((1, 0, 0)), lattice.vec((0, 1, 0)), lattice.vec((0, 0, 1)) ) [....] #Hall bar def onsite(site, B): (x, y, z) = site.pos return stored_model[site] def hopping_Ax(site1, site2, B): x1, y1, z1 = site1.pos x2, y2, z2 = site2.pos return stored_model[site1,site2] * np.exp(0.5j * B * (x1 + x2) * (y1  y2)) kwant_model[lattice.shape(shape, (0, 0, 15))] = onsite kwant_model[lattice.neighbors()] = hopping_Ax kwant_sys = wraparound.wraparound(kwant_model).finalized() B = 0.02 # Obtain the Hamiltonian as a dense matrix ham_mat = kwant_sys.hamiltonian_submatrix(args=[B], sparse=True)  TypeError Traceback (most recent call last) ~\Anaconda3\lib\sitepackages\kwant\builder.py in hamiltonian(self, i, j, params, *args) 2000 try: > 2001 value = value(self.sites[i], *args) 2002 except Exception as exc: ~\Anaconda3\lib\sitepackages\wraparound.py in <lambda>(*args) 81 return lambda *args: sum((val(*args) if callable(val) else val) > 82 for val in vals) 83 ~\Anaconda3\lib\sitepackages\wraparound.py in <genexpr>(.0) 81 return lambda *args: sum((val(*args) if callable(val) else val) > 82 for val in vals) 83 ~\Anaconda3\lib\sitepackages\wraparound.py in <lambda>(a, *args) 59 assert callable(val) > 60 return lambda a, *args: val(a, *args[:mnp]) 61 TypeError: onsite() missing 1 required positional argument: 'B' The above exception was the direct cause of the following exception: UserCodeError Traceback (most recent call last) <ipythoninput19dd56ba85dfde> in <module>() 1 B = 0.02 2 # Obtain the Hamiltonian as a dense matrix > 3 ham_mat = kwant_sys.hamiltonian_submatrix(args=[B], sparse=True) 4 kwant\_system.pyx in kwant._system.hamiltonian_submatrix() ~\Anaconda3\lib\sitepackages\kwant\builder.py in hamiltonian(self, i, j, params, *args) 2001 value = value(self.sites[i], *args) 2002 except Exception as exc: > 2003 _raise_user_error(exc, value) 2004 else: 2005 edge_id = self.graph.first_edge_id(i, j) ~\Anaconda3\lib\sitepackages\kwant\builder.py in _raise_user_error(exc, func) 1883 msg = ('Error occurred in usersupplied value function "{0}".\n' 1884 'See the upper part of the above backtrace for more information.') > 1885 raise UserCodeError(msg.format(func.__name__)) from exc 1886 1887 UserCodeError: Error occurred in usersupplied value function "<lambda>". See the upper part of the above backtrace for more information.  Eleni Quoting elchatz@auth.gr:
Hello Joseph,
Thank you. It is working when I copy the model and each lead after I have attached them.
Regards,
Eleni
Quoting Joseph Weston <joseph.weston08@gmail.com>:
HI,
I am trying to reproduce the QHE bar device calculations
http://nbviewer.jupyter.org/github/topocm/topocm_content/blob/master/w3_pump...
However, I am having difficulty with the onsite and hopping values as I am using TBModels
https://github.com/Z2PackDev/TBmodels
and therefore the values are not the same for all sites.
I am unsure of the output format of TBModels. Glancing at their documentation I can't see any way of getting the raw matrix elements from a "Model". Looking into the source code it seems that they are stored in a format that will be annoying to query manually.
The problem is that after the scalar values have been passed on to the Builder, these will then be overriden when using functions for the positiondependent Hamiltonian.
I tried making a deep copy of the model, which would then serve as a data structure where to draw the scalar values from when calling the Onsite and Hopping functions. The problem with this is
a) I am getting a KeyError which I am still not sure why it happens b) It does not feel very memoryefficient.
I am wondering if there is another way that this could be done on the Kwant side that I have not been able to think of.
I can't think of a better way to accomplish this. Using TBModels' internal datastructures directly is IMO too much hassle unless your systems are really big.
Did you check that the symmetry of your Kwant system and the TBModels Model are compatible?
Joe
 Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz@auth.gr  tel:+30 2310 998109
 Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz@auth.gr  tel:+30 2310 998109
Hi
sym = kwant.TranslationalSymmetry( lattice.vec((1, 0, 0)), lattice.vec((0, 1, 0)), lattice.vec((0, 0, 1)) )
[....]
#Hall bar def onsite(site, B): (x, y, z) = site.pos return stored_model[site]
def hopping_Ax(site1, site2, B): x1, y1, z1 = site1.pos x2, y2, z2 = site2.pos return stored_model[site1,site2] * np.exp(0.5j * B * (x1 + x2) * (y1  y2))
kwant_model[lattice.shape(shape, (0, 0, 15))] = onsite kwant_model[lattice.neighbors()] = hopping_Ax
kwant_sys = wraparound.wraparound(kwant_model).finalized()
B = 0.02 # Obtain the Hamiltonian as a dense matrix ham_mat = kwant_sys.hamiltonian_submatrix(args=[B], sparse=True)
The docstring for 'wraparound' [1] says that the wrapped around system will have additional parameters, corresponding to the momenta. As you have a 3D system and have wrapped around all 3 dimensions, the parameters will be 'k_x', 'k_y', and 'k_z'. As you have only supplied a single argument (B) to your system, an error is raised. You will need to provide all the arguments to your system: kwant_sys.hamiltonian_submatrix(params=dict(k_x=0, k_y=0, k_z=0, B=B), sparse=True) Happy Kwanting, Joe [1]: https://kwantproject.org/doc/1/reference/generated/kwant.wraparound.wraparo...
Hello Joseph, Thank you for replying. I still can't make this work.  ham_mat = kwant_sys.hamiltonian_submatrix(params=dict(k_x=0, k_y=0, k_z=0, B=0.02), sparse=True)  ValueError Traceback (most recent call last) ~\Anaconda3\lib\sitepackages\kwant\builder.py in hamiltonian(self, i, j, params, *args) 1995 try: > 1996 value = value(self.sites[i], **params) 1997 except Exception as exc: ~\Anaconda3\lib\sitepackages\wraparound.py in <lambda>(*args) 81 return lambda *args: sum((val(*args) if callable(val) else val) > 82 for val in vals) 83 ~\Anaconda3\lib\sitepackages\wraparound.py in <genexpr>(.0) 81 return lambda *args: sum((val(*args) if callable(val) else val) > 82 for val in vals) 83 ~\Anaconda3\lib\sitepackages\wraparound.py in f(a, *args) 64 def f(a, *args): > 65 phase = cmath.exp(1j * ta.dot(elem, args[mnp:])) 66 v = val(a, sym.act(elem, a), *args[:mnp]) if callable(val) else val ValueError: Both arguments must have same length. The above exception was the direct cause of the following exception: UserCodeError Traceback (most recent call last) <ipythoninput27326c257cc228> in <module>() > 1 ham_mat = kwant_sys.hamiltonian_submatrix(params=dict(k_x=0, k_y=0, k_z=0, B=0.02), sparse=True) kwant\_system.pyx in kwant._system.hamiltonian_submatrix() ~\Anaconda3\lib\sitepackages\kwant\builder.py in hamiltonian(self, i, j, params, *args) 1996 value = value(self.sites[i], **params) 1997 except Exception as exc: > 1998 _raise_user_error(exc, value) 1999 else: 2000 try: ~\Anaconda3\lib\sitepackages\kwant\builder.py in _raise_user_error(exc, func) 1883 msg = ('Error occurred in usersupplied value function "{0}".\n' 1884 'See the upper part of the above backtrace for more information.') > 1885 raise UserCodeError(msg.format(func.__name__)) from exc 1886 1887 UserCodeError: Error occurred in usersupplied value function "<lambda>". See the upper part of the above backtrace for more information.  Eleni Quoting Joseph Weston <joseph.weston08@gmail.com>:
Hi
sym = kwant.TranslationalSymmetry( lattice.vec((1, 0, 0)), lattice.vec((0, 1, 0)), lattice.vec((0, 0, 1)) )
[....]
#Hall bar def onsite(site, B): (x, y, z) = site.pos return stored_model[site]
def hopping_Ax(site1, site2, B): x1, y1, z1 = site1.pos x2, y2, z2 = site2.pos return stored_model[site1,site2] * np.exp(0.5j * B * (x1 + x2) * (y1  y2))
kwant_model[lattice.shape(shape, (0, 0, 15))] = onsite kwant_model[lattice.neighbors()] = hopping_Ax
kwant_sys = wraparound.wraparound(kwant_model).finalized()
B = 0.02 # Obtain the Hamiltonian as a dense matrix ham_mat = kwant_sys.hamiltonian_submatrix(args=[B], sparse=True)
The docstring for 'wraparound' [1] says that the wrapped around system will have additional parameters, corresponding to the momenta. As you have a 3D system and have wrapped around all 3 dimensions, the parameters will be 'k_x', 'k_y', and 'k_z'.
As you have only supplied a single argument (B) to your system, an error is raised. You will need to provide all the arguments to your system:
kwant_sys.hamiltonian_submatrix(params=dict(k_x=0, k_y=0, k_z=0, B=B), sparse=True)
Happy Kwanting,
Joe
[1]: https://kwantproject.org/doc/1/reference/generated/kwant.wraparound.wraparo...
 Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz@auth.gr  tel:+30 2310 998109
Hello, Just as a note I chose a system with no symmetry (and no leads) to check the spectrum which gives no errors and is easier to work with. I used the code from the tutorial\closed_system.py The subtle point here was that: When defining a shape (with no symmetry), all three dimensions of the system need to be defined otherwise TBModels hangs. Regards, Eleni Quoting elchatz@auth.gr:
Hello Joseph,
Thank you for replying. I still can't make this work.
 ham_mat = kwant_sys.hamiltonian_submatrix(params=dict(k_x=0, k_y=0, k_z=0, B=0.02), sparse=True)  ValueError Traceback (most recent call last) ~\Anaconda3\lib\sitepackages\kwant\builder.py in hamiltonian(self, i, j, params, *args) 1995 try: > 1996 value = value(self.sites[i], **params) 1997 except Exception as exc:
~\Anaconda3\lib\sitepackages\wraparound.py in <lambda>(*args) 81 return lambda *args: sum((val(*args) if callable(val) else val) > 82 for val in vals) 83
~\Anaconda3\lib\sitepackages\wraparound.py in <genexpr>(.0) 81 return lambda *args: sum((val(*args) if callable(val) else val) > 82 for val in vals) 83
~\Anaconda3\lib\sitepackages\wraparound.py in f(a, *args) 64 def f(a, *args): > 65 phase = cmath.exp(1j * ta.dot(elem, args[mnp:])) 66 v = val(a, sym.act(elem, a), *args[:mnp]) if callable(val) else val
ValueError: Both arguments must have same length.
The above exception was the direct cause of the following exception:
UserCodeError Traceback (most recent call last) <ipythoninput27326c257cc228> in <module>() > 1 ham_mat = kwant_sys.hamiltonian_submatrix(params=dict(k_x=0, k_y=0, k_z=0, B=0.02), sparse=True)
kwant\_system.pyx in kwant._system.hamiltonian_submatrix()
~\Anaconda3\lib\sitepackages\kwant\builder.py in hamiltonian(self, i, j, params, *args) 1996 value = value(self.sites[i], **params) 1997 except Exception as exc: > 1998 _raise_user_error(exc, value) 1999 else: 2000 try:
~\Anaconda3\lib\sitepackages\kwant\builder.py in _raise_user_error(exc, func) 1883 msg = ('Error occurred in usersupplied value function "{0}".\n' 1884 'See the upper part of the above backtrace for more information.') > 1885 raise UserCodeError(msg.format(func.__name__)) from exc 1886 1887
UserCodeError: Error occurred in usersupplied value function "<lambda>". See the upper part of the above backtrace for more information. 
Eleni
Quoting Joseph Weston <joseph.weston08@gmail.com>:
Hi
sym = kwant.TranslationalSymmetry( lattice.vec((1, 0, 0)), lattice.vec((0, 1, 0)), lattice.vec((0, 0, 1)) )
[....]
#Hall bar def onsite(site, B): (x, y, z) = site.pos return stored_model[site]
def hopping_Ax(site1, site2, B): x1, y1, z1 = site1.pos x2, y2, z2 = site2.pos return stored_model[site1,site2] * np.exp(0.5j * B * (x1 + x2) * (y1  y2))
kwant_model[lattice.shape(shape, (0, 0, 15))] = onsite kwant_model[lattice.neighbors()] = hopping_Ax
kwant_sys = wraparound.wraparound(kwant_model).finalized()
B = 0.02 # Obtain the Hamiltonian as a dense matrix ham_mat = kwant_sys.hamiltonian_submatrix(args=[B], sparse=True)
The docstring for 'wraparound' [1] says that the wrapped around system will have additional parameters, corresponding to the momenta. As you have a 3D system and have wrapped around all 3 dimensions, the parameters will be 'k_x', 'k_y', and 'k_z'.
As you have only supplied a single argument (B) to your system, an error is raised. You will need to provide all the arguments to your system:
kwant_sys.hamiltonian_submatrix(params=dict(k_x=0, k_y=0, k_z=0, B=B), sparse=True)
Happy Kwanting,
Joe
[1]: https://kwantproject.org/doc/1/reference/generated/kwant.wraparound.wraparo...
 Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz@auth.gr  tel:+30 2310 998109
 Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz@auth.gr  tel:+30 2310 998109
Hello again, For the translation vectors, I managed to do some progress. I don't know how I should declare by arguments so that they get where they are supposed to. Here is what I have until now:  kwant_model = kwant.Builder() kwant_model[lattice.shape(shape, (0, 0, 15))] = 0 model.add_hoppings_kwant(kwant_model) def onsite(site, params=dict(B=0, k_x=0, k_y=0, k_z=0)): return kwant_model[site] def hopx(site1, site2, params=dict(B=0, k_x=0, k_y=0, k_z=0)): x1, y1, z1 = site1.pos x2, y2, z2 = site2.pos for key, value in params.items(): if key == 'B': B=value return kwant_model[site1,site2] * np.exp(0.5j * B * (x1 + x2) * (y1  y2)) #Make a new model pointing in the previous model new_model = kwant.Builder(sym) #Change the onsite elements new_model[lattice.shape(shape, (0, 0, 15))] = onsite #Change the lattice hoppings for i in (range(len(lattice.sublattices))): kwant_model[lattice.sublattices[i].neighbors()] = hopx for R, mat in model.hop.items(): dir = tuple(np.array(R)) for i, s1 in enumerate(lattice.sublattices): for j, s2 in enumerate(lattice.sublattices): if i !=j: new_model[kwant.builder.HoppingKind(dir, lattice.sublattices[i],lattice.sublattices[j])] = hopx # Finalize the system. sys = wraparound.wraparound(new_model).finalized()  But I am still getting errors. So my questions are: 1) Do I have to use a dictionary in the onsite and hopping function definitions? From what I understand, if I only use the B argument, maybe it gets 'eaten' in the memoize and I get a 'missing positional arguments error'. 2) What do you think the symmetry of the original model should be and what of the new_model so that I can write on the momentum operator arguments properly? Kind Regards, Eleni Quoting Joseph Weston <joseph.weston08@gmail.com>:
Hi
sym = kwant.TranslationalSymmetry( lattice.vec((1, 0, 0)), lattice.vec((0, 1, 0)), lattice.vec((0, 0, 1)) )
[....]
#Hall bar def onsite(site, B): (x, y, z) = site.pos return stored_model[site]
def hopping_Ax(site1, site2, B): x1, y1, z1 = site1.pos x2, y2, z2 = site2.pos return stored_model[site1,site2] * np.exp(0.5j * B * (x1 + x2) * (y1  y2))
kwant_model[lattice.shape(shape, (0, 0, 15))] = onsite kwant_model[lattice.neighbors()] = hopping_Ax
kwant_sys = wraparound.wraparound(kwant_model).finalized()
B = 0.02 # Obtain the Hamiltonian as a dense matrix ham_mat = kwant_sys.hamiltonian_submatrix(args=[B], sparse=True)
The docstring for 'wraparound' [1] says that the wrapped around system will have additional parameters, corresponding to the momenta. As you have a 3D system and have wrapped around all 3 dimensions, the parameters will be 'k_x', 'k_y', and 'k_z'.
As you have only supplied a single argument (B) to your system, an error is raised. You will need to provide all the arguments to your system:
kwant_sys.hamiltonian_submatrix(params=dict(k_x=0, k_y=0, k_z=0, B=B), sparse=True)
Happy Kwanting,
Joe
[1]: https://kwantproject.org/doc/1/reference/generated/kwant.wraparound.wraparo...
 Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz@auth.gr  tel:+30 2310 998109
participants (2)

elchatz＠auth.gr

Joseph Weston