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ensuring Hermitian hopping

Sergey

6 May 2016 6 May '16

1:18 a.m.

Dear all, I want to model a random variation of hopping integrals. Simply writing: def hopping(sitei, sitej): return -1 + random.gauss(0,0.2) does not work since this does not ensure that the hopping is Hermitian. Is there a smart way to write something like: def hopping(sitei, sitej): if sitei

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Anton Akhmerov

6 May 6 May

2:23 a.m.

Hi Sergey, Quoting from http://kwant-project.org/doc/1/reference/generated/kwant.builder.Builder#kwa...:

...

Builder instances automatically ensure that every hopping is Hermitian, so that if builder[a, b] has been set, there is no need to set builder[b, a].

So you don't need to pay any extra effort to ensure hermiticity. However your code has a different minor drawback. The order in which the hoppings are evaluated in Kwant is not deterministic, so you will get random results that you are unable to reevaluate. You could avoid this by using the hash-based random number generators provided by kwant.digest. See e.g. code here for an example of use http://arxiv.org/src/1408.1563v2/anc/trijunction.py (the "disorder" function). Best, Anton On Thu, May 5, 2016 at 9:48 PM, Sergey wrote:

...

Dear all, I want to model a random variation of hopping integrals. Simply writing:

def hopping(sitei, sitej): return -1 + random.gauss(0,0.2)

does not work since this does not ensure that the hopping is Hermitian. Is there a smart way to write something like: def hopping(sitei, sitej): if sitei
? Thanks and best wishes, Sergey

Sergey

3:58 a.m.

On 05/05/16 21:53, Anton Akhmerov wrote:

...

Hi Sergey,

...
Builder instances automatically ensure that every hopping is Hermitian, so that if builder[a, b] has been set, there is no need to set builder[b, a]. So you don't need to pay any extra effort to ensure hermiticity. However your code has a different minor drawback. The order in which

Quoting from http://kwant-project.org/doc/1/reference/generated/kwant.builder.Builder#kwa...: the hoppings are evaluated in Kwant is not deterministic, so you will get random results that you are unable to reevaluate. You could avoid this by using the hash-based random number generators provided by kwant.digest. See e.g. code here for an example of use http://arxiv.org/src/1408.1563v2/anc/trijunction.py (the "disorder" function).

Best, Anton

On Thu, May 5, 2016 at 9:48 PM, Sergey wrote:

...
Dear all, I want to model a random variation of hopping integrals. Simply writing:

def hopping(sitei, sitej): return -1 + random.gauss(0,0.2)

does not work since this does not ensure that the hopping is Hermitian. Is there a smart way to write something like: def hopping(sitei, sitej): if sitei
? Thanks and best wishes, Sergey

Anton Akhmerov

2:54 p.m.

Hi Sergey, Let me put it differently: it is pretty much impossible to make a hopping non-hermitian. If you set both the hopping (a, b) and (b, a) then, the second one will just supercede the first. If you look at the source code of Kwant, you'll see that exactly what you want is already happening (only it doesn't check which site number is larger, but checks which hopping was assigned directly (with the opposite hopping being the hermitian conjugate). Additionally, pretty much every tutorial sets hoppings in only one direction. You write "And that clearly leads to errors." why are you sure? Did you try to evaluate the system Hamiltonian and see if it is hermitian? Cheers, Anton On Fri, May 6, 2016 at 12:28 AM, Sergey wrote:

...

On 05/05/16 21:53, Anton Akhmerov wrote:

...
Hi Sergey,

Quoting from http://kwant-project.org/doc/1/reference/generated/kwant.builder.Builder#kwa...:

...
Builder instances automatically ensure that every hopping is Hermitian, so that if builder[a, b] has been set, there is no need to set builder[b, a].

So you don't need to pay any extra effort to ensure hermiticity. However your code has a different minor drawback. The order in which the hoppings are evaluated in Kwant is not deterministic, so you will get random results that you are unable to reevaluate. You could avoid this by using the hash-based random number generators provided by kwant.digest. See e.g. code here for an example of use http://arxiv.org/src/1408.1563v2/anc/trijunction.py (the "disorder" function).

Best, Anton

On Thu, May 5, 2016 at 9:48 PM, Sergey wrote:

...
Dear all, I want to model a random variation of hopping integrals. Simply writing:

def hopping(sitei, sitej): return -1 + random.gauss(0,0.2)

does not work since this does not ensure that the hopping is Hermitian. Is there a smart way to write something like: def hopping(sitei, sitej): if sitei
? Thanks and best wishes, Sergey

Sergey

11 May 11 May

2:48 a.m.

Hi Anton, Somehow I again start to get 'The cell Hamiltonian is not Hermitian.' error raised by dispersion.py (for band structure of a lead). Although I have ensured that hoppings are hermitian and respect the lead translation symmetry. I have not used any low-level functions, so, it's a bit strange to get such a error. Is that a tolerance issue? Best wishes, Sergey On 06/05/16 10:24, Anton Akhmerov wrote:

...

Hi Sergey,

Let me put it differently: it is pretty much impossible to make a hopping non-hermitian. If you set both the hopping (a, b) and (b, a) then, the second one will just supercede the first. If you look at the source code of Kwant, you'll see that exactly what you want is already happening (only it doesn't check which site number is larger, but checks which hopping was assigned directly (with the opposite hopping being the hermitian conjugate). Additionally, pretty much every tutorial sets hoppings in only one direction.

You write "And that clearly leads to errors." why are you sure? Did you try to evaluate the system Hamiltonian and see if it is hermitian?

Cheers, Anton

On Fri, May 6, 2016 at 12:28 AM, Sergey wrote:

...
On 05/05/16 21:53, Anton Akhmerov wrote:

...
Hi Sergey,

...
Builder instances automatically ensure that every hopping is Hermitian, so that if builder[a, b] has been set, there is no need to set builder[b, a]. So you don't need to pay any extra effort to ensure hermiticity. However your code has a different minor drawback. The order in which

Quoting from http://kwant-project.org/doc/1/reference/generated/kwant.builder.Builder#kwa...: the hoppings are evaluated in Kwant is not deterministic, so you will get random results that you are unable to reevaluate. You could avoid this by using the hash-based random number generators provided by kwant.digest. See e.g. code here for an example of use http://arxiv.org/src/1408.1563v2/anc/trijunction.py (the "disorder" function).

Best, Anton

On Thu, May 5, 2016 at 9:48 PM, Sergey wrote:

...
Dear all, I want to model a random variation of hopping integrals. Simply writing:

def hopping(sitei, sitej): return -1 + random.gauss(0,0.2)

does not work since this does not ensure that the hopping is Hermitian. Is there a smart way to write something like: def hopping(sitei, sitej): if sitei
? Thanks and best wishes, Sergey

Abbout Adel

3:38 a.m.

Dear Sergey, If you print the hoppings of an unfinalized system: print [hop for hop in sys.hoppings()] #sys here is unfinalized you will notice that if the hopping (site1, site2) is present then (site2, site1) will be absent (check it for a small system). This shows you that the other hopping is fixed by hermeticity in kwant programs. The error you get in your program has a different origin which is not related to kwant: The argument of arctanh in your program is wrong : it should be in the interval [-1, 1]. correct this and your program will work fine. Best regards Adel On Wed, May 11, 2016 at 12:18 AM, Sergey wrote:

...

Hi Anton, Somehow I again start to get 'The cell Hamiltonian is not Hermitian.' error raised by dispersion.py (for band structure of a lead). Although I have ensured that hoppings are hermitian and respect the lead translation symmetry. I have not used any low-level functions, so, it's a bit strange to get such a error. Is that a tolerance issue?

Best wishes, Sergey

On 06/05/16 10:24, Anton Akhmerov wrote:

...
Hi Sergey,

Let me put it differently: it is pretty much impossible to make a hopping non-hermitian. If you set both the hopping (a, b) and (b, a) then, the second one will just supercede the first. If you look at the source code of Kwant, you'll see that exactly what you want is already happening (only it doesn't check which site number is larger, but checks which hopping was assigned directly (with the opposite hopping being the hermitian conjugate). Additionally, pretty much every tutorial sets hoppings in only one direction.

You write "And that clearly leads to errors." why are you sure? Did you try to evaluate the system Hamiltonian and see if it is hermitian?

Cheers, Anton

On Fri, May 6, 2016 at 12:28 AM, Sergey wrote:

...
On 05/05/16 21:53, Anton Akhmerov wrote:

...
Hi Sergey,

Quoting from

http://kwant-project.org/doc/1/reference/generated/kwant.builder.Builder#kwa... :

...
Builder instances automatically ensure that every hopping is Hermitian, so that if builder[a, b] has been set, there is no need to set builder[b, a].

So you don't need to pay any extra effort to ensure hermiticity. However your code has a different minor drawback. The order in which the hoppings are evaluated in Kwant is not deterministic, so you will get random results that you are unable to reevaluate. You could avoid this by using the hash-based random number generators provided by kwant.digest. See e.g. code here for an example of use http://arxiv.org/src/1408.1563v2/anc/trijunction.py (the "disorder" function).

Best, Anton

On Thu, May 5, 2016 at 9:48 PM, Sergey wrote:

...
Dear all, I want to model a random variation of hopping integrals. Simply writing:

def hopping(sitei, sitej): return -1 + random.gauss(0,0.2)

does not work since this does not ensure that the hopping is Hermitian. Is there a smart way to write something like: def hopping(sitei, sitej): if sitei
? Thanks and best wishes, Sergey

-- Abbout Adel

Joseph Weston

3:40 a.m.

Hi, I ran your script and the first line output is: SnakesStripe.py:31: RuntimeWarning: invalid value encountered in arctanh return -exp(-0.5j * phi * (xi - xj) * arctanh(((yi + yj)-2*45*sqrt(3))/smooth)) You are passing a number >1 to `arctanh`, most probably. You're using Numpy's arctanh, which just shows a warning and returns `nan`, if I replace `numpy.arctanh` with the `math` module's `atanh` I get ValueError: math domain error which corroborates my explanation. Happy Kwanting, Joe On 10 May 2016 at 23:18, Sergey wrote:

...

Hi Anton, Somehow I again start to get 'The cell Hamiltonian is not Hermitian.' error raised by dispersion.py (for band structure of a lead). Although I have ensured that hoppings are hermitian and respect the lead translation symmetry. I have not used any low-level functions, so, it's a bit strange to get such a error. Is that a tolerance issue?

Best wishes, Sergey

On 06/05/16 10:24, Anton Akhmerov wrote:

...
Hi Sergey,

Let me put it differently: it is pretty much impossible to make a hopping non-hermitian. If you set both the hopping (a, b) and (b, a) then, the second one will just supercede the first. If you look at the source code of Kwant, you'll see that exactly what you want is already happening (only it doesn't check which site number is larger, but checks which hopping was assigned directly (with the opposite hopping being the hermitian conjugate). Additionally, pretty much every tutorial sets hoppings in only one direction.

You write "And that clearly leads to errors." why are you sure? Did you try to evaluate the system Hamiltonian and see if it is hermitian?

Cheers, Anton

On Fri, May 6, 2016 at 12:28 AM, Sergey wrote:

...
On 05/05/16 21:53, Anton Akhmerov wrote:

...
Hi Sergey,

Quoting from

http://kwant-project.org/doc/1/reference/generated/kwant.builder.Builder#kwa... :

...
Builder instances automatically ensure that every hopping is Hermitian, so that if builder[a, b] has been set, there is no need to set builder[b, a].

So you don't need to pay any extra effort to ensure hermiticity. However your code has a different minor drawback. The order in which the hoppings are evaluated in Kwant is not deterministic, so you will get random results that you are unable to reevaluate. You could avoid this by using the hash-based random number generators provided by kwant.digest. See e.g. code here for an example of use http://arxiv.org/src/1408.1563v2/anc/trijunction.py (the "disorder" function).

Best, Anton

On Thu, May 5, 2016 at 9:48 PM, Sergey wrote:

...
Dear all, I want to model a random variation of hopping integrals. Simply writing:

def hopping(sitei, sitej): return -1 + random.gauss(0,0.2)

does not work since this does not ensure that the hopping is Hermitian. Is there a smart way to write something like: def hopping(sitei, sitej): if sitei
? Thanks and best wishes, Sergey

Sergey

12:27 p.m.

Thank you! and sorry for stupid question. Indeed, I have not noticed the real origin of the error! Best wishes, Sergey On 10/05/16 23:10, Joseph Weston wrote:

...

Hi,

I ran your script and the first line output is:

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Abbout Adel
Anton Akhmerov
Anton Akhmerov
Joseph Weston
Sergey

ensuring Hermitian hopping

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