Implementation of fermionic hilbert and operator #1090

jwnys · 2022-01-31T12:27:41Z

This is an implementation of discrete fermionic degrees of freedom by @imi-hub and myself.
It contains the hilbert space and an operator. The operator handles the minus signs coming from the exchange symmetry, while the hilbert space stores occupation numbers only. This follows e.g. the way qiskit and openfermion would implement things.
For the operator, we follow the implementation of openfermion and added an 'from_openfermion' function to create operators. This allows us to use all their hamiltonians, such as Fermi-Hubbard.
The hilbert space is not optimized for fixed number of fermions (since it inherits from HomogeneousHilbert), for that we might need to add another Hilbert implementation.

FYI: formatting will fail because flake8 and flakehell are giving me hell.

gcarleo · 2022-01-31T12:32:58Z

The hilbert space is not optimized for fixed number of fermions (since it inherits from HomogeneousHilbert), for that we might need to add another Hilbert implementation.

don't we already have some kind of support for that for fock spaces? (actually, I would tend to say we can use the already existing fock hilbert without creating a new one? maybe I am mistaken...!)

gcarleo · 2022-01-31T12:33:50Z

what I mean is: can't you derive Fermions2nd from Fock directly?

jwnys · 2022-01-31T12:35:02Z

Good point, I'll look into that

PhilipVinc · 2022-01-31T12:37:09Z

Can we be careful about that and discuss it briefly in person?

While I know it's possible to inherit from a non abstract class, I'd be wary of it because it has been a source of bugs in the past.

I'd prefer if in general non abstract things where not inherited from.

gcarleo · 2022-01-31T12:55:19Z

I'd prefer if in general non abstract things where not inherited from.

sure, actually I just meant to construct a Fock space, not inherit from it

jwnys · 2022-01-31T13:09:26Z

What do you mean, creating a class Fermions2nd which has a self._fock as field?

gcarleo · 2022-01-31T13:11:18Z

no I just suspect you can construct the object just by returning Fock(something), do you need extra methods that are not in fock?

codecov-commenter · 2022-01-31T13:12:40Z

Codecov Report

Merging #1090 (19f3c25) into master (53769ed) will increase coverage by 0.14%.
The diff coverage is 76.18%.

@@            Coverage Diff             @@
##           master    #1090      +/-   ##
==========================================
+ Coverage   81.77%   81.91%   +0.14%     
==========================================
  Files         199      208       +9     
  Lines       12015    12526     +511     
  Branches     1800     1897      +97     
==========================================
+ Hits         9825    10261     +436     
- Misses       1762     1817      +55     
- Partials      428      448      +20

Impacted Files	Coverage Δ
netket/experimental/operator/_fermions_2nd.py	`73.22% <73.22%> (ø)`
netket/experimental/operator/fermion.py	`76.92% <76.92%> (ø)`
...tket/experimental/hilbert/spin_orbital_fermions.py	`85.33% <85.33%> (ø)`
...perimental/hilbert/random/spin_orbital_fermions.py	`90.90% <90.90%> (ø)`
netket/experimental/__init__.py	`100.00% <100.00%> (ø)`
netket/experimental/hilbert/__init__.py	`100.00% <100.00%> (ø)`
netket/experimental/hilbert/random/__init__.py	`100.00% <100.00%> (ø)`
netket/experimental/operator/__init__.py	`100.00% <100.00%> (ø)`
netket/operator/_local_operator.py	`64.15% <0.00%> (-4.28%)`	⬇️
netket/operator/_graph_operator.py	`83.05% <0.00%> (-1.70%)`	⬇️
... and 7 more

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jwnys · 2022-01-31T13:14:48Z

Well, the idea is mostly to (in the next step) optimize this for fixed number of fermions, since that's relevant for 99% of all cases. I guess that would be less obvious with Fock?

test/operator/test_operator.py

gcarleo · 2022-01-31T13:18:41Z

Well, the idea is mostly to (in the next step) optimize this for fixed number of fermions, since that's relevant for 99% of all cases. I guess that would be less obvious with Fock?

but Fock is already optimized for fixed number of particles, as far as I remember (not sure why N is referred to as the number of bosonic modes in the docs though, since it's more general)

        Args:
          n_max: Maximum occupation for a site (inclusive). If None, the local
            occupation number is unbounded.
          N: number of bosonic modes (default = 1)
          n_particles: Constraint for the number of particles. If None, no constraint
            is imposed.
          graph: (Deprecated, pleaese use `N`) A graph, from which the number of nodes
            is extracted.

gcarleo · 2022-01-31T13:22:02Z

I would say that Fock(n_max=1, N=n_sites,n_particles=n_fermions) is already the fock space for spinless fermions at fixed number of particles... then if you have two orbitals just take the tensor product of two fock states etc?

PhilipVinc · 2022-01-31T14:25:30Z

~~girls/guys~~ people something happened and i see tons of commits around and stuff that i think is not related?
Can you please clean it up?

jwnys · 2022-01-31T14:58:36Z

Should be ok now.

PhilipVinc · 2022-01-31T15:08:16Z

By the way, if we are going to merge this in NetKet, i'd like to have this live for at least a few months in import netket.experimental as nkx for a while, while the interface gets refined by... you guys.

jwnys · 2022-01-31T16:10:21Z

Well, the idea is mostly to (in the next step) optimize this for fixed number of fermions, since that's relevant for 99% of all cases. I guess that would be less obvious with Fock?

but Fock is already optimized for fixed number of particles, as far as I remember (not sure why N is referred to as the number of bosonic modes in the docs though, since it's more general)
        Args:
          n_max: Maximum occupation for a site (inclusive). If None, the local
            occupation number is unbounded.
          N: number of bosonic modes (default = 1)
          n_particles: Constraint for the number of particles. If None, no constraint
            is imposed.
          graph: (Deprecated, pleaese use `N`) A graph, from which the number of nodes
            is extracted.

Fock uses the constraint function to impose the number of particles, so it enumerates them all and then removes the incorrect ones, if I understand correctly. What do we gain from inheriting from Fock and not Homogeneous? I don't see much gain...
So, the idea (after talking to Filippo) is now to keep inheriting from HomogeneousHilbert and to just overwrite all the correct _numbers_to_states etc. stuff if we want to optimize for fixed number of fermions. I'm not the biggest fan of this API, but I agree it makes conceptually more sense.

jwnys · 2022-01-31T16:14:11Z

By the way, if we are going to merge this in NetKet, i'd like to have this live for at least a few months in import netket.experimental as nkx for a while, while the interface gets refined by... you guys.

I will do this once we agree on the hilbert and operator concept, have a all the minimal implementations, etc.

PhilipVinc · 2022-01-31T17:57:21Z

The problem is that the api of _constraint_fn, which is quite ugly, has never been thought to be completely overriden.
We should revisit that part of the API a bit...

It goes back to netket 1

jwnys · 2022-02-04T08:40:39Z

One thing I realized is the following: in this representation, if you do a translation operator for example, you need to define the parity of such an operator. So e.g. if you order your original sites as (0, 1, 2, 3) in some way (e.g. zigzag), then the translation brings this (on a 2x2 lattice) to (1, 0, 3, 2) for example. You then need to compute the parity of the (1, 0, 3, 2) permutation to determine the representation of this transformation in the given basis. This might be a bit annoying, but maybe it's fine if we just add some functions that can quickly compute the parity of such transformations. Alternatively, we define an additional operator type that does this. What do you think?

PhilipVinc · 2022-02-04T08:44:12Z

Can you say something more about why you'd need me he parity? Where?

jwnys · 2022-02-04T08:48:33Z

This would be when you want to look at excitations, for example. Maybe it's not necessary to define it, but it might also be tricky because it's not a priori clear in this representation that you need such parity factors.

gcarleo · 2022-02-04T08:53:00Z

@jwnys yes I understand the issue, but I am not sure why you need this to be defined in the operator itself? (as far as I know we do not support transforming operators with symmetries, even for spins?)

gcarleo · 2022-02-04T08:55:28Z

what I am trying to say here is that we should think about more broadly about supporting symmetry transformations for operators/ quickly identifying the correct phase, but I think it's best to separate the discussion and do that in another PR?

jwnys · 2022-02-04T08:57:21Z

what I am trying to say here is that we should think about more broadly about supporting symmetry transformations for operators/ quickly identifying the correct phase, but I think it's best to separate the discussion and do that in another PR?

Ok, that makes sense, yeah. Thanks for the feedback.

gcarleo · 2022-02-04T08:58:08Z

Still, I am a bit unconvinced by the fact that we cannot derive/ construct this directly from Fock, since both the constraints and the local occupation numbers you need are exactly the same you already have there. Aren't we just going to duplicate the code to fix the total number of particles, for example?

jwnys · 2022-02-04T09:02:36Z

Still, I am a bit unconvinced by the fact that we cannot derive/ construct this directly from Fock, since both the constraints and the local occupation numbers you need are exactly the same you already have there. Aren't we just going to duplicate the code to fix the total number of particles, for example?

I don't really have a very strong opinion on this. It might be ok to do it like that. What I had in mind for fixed particles was to construct the hilbert states in blocks of fixed number of fermions. In that case the ordering would be rather different from e.g. Fock where you list all possibilities and just delete the ones that violate the constraint. The advantage would be that you can do ED for bigger systems. However, the disadvantage would be that our matrix then looks quite different from other libraries, since the convention of ordering the states would be different.
In any case, maybe we could just leave this for later and use Fock for now.

gcarleo

a few points in the API I guess need to be clarified, but otherwise it's good! can we also maybe add a small example (say, Hubbard model or spinless fermions) or even (ideally, if you or Imelda have time) a tutorial with ED?

netket/hilbert/fermions_2nd.py

jwnys · 2022-02-13T16:06:35Z

To summarize, the new version: it's a lot faster for symbolic operations and implements many more things like iadd, etc (following the new implementation of LocalOperator by @PhilipVinc ).
I've changed the spin=None default argument and made some more small changes. I think this version is close to final for now.

netket/experimental/operator/_fermions_2nd.py

Examples/Fermions/fermi_hubbard.py

PhilipVinc

some more stuff

netket/experimental/operator/_fermions_2nd.py

PhilipVinc

Ok, there's only a few missing tests and we're ready to merge.

netket/experimental/operator/fermion.py

netket/experimental/operator/_fermions_2nd.py

PhilipVinc

Seems good to me now.

PhilipVinc · 2022-02-15T13:03:49Z

Assuming tests pass*

PhilipVinc · 2022-02-15T18:07:17Z

Tests pass, so this can be merged now.
@jwnys Could you just add the new hilbert space and operator to the documentation, under the experimental section? the file is 'docs/docs/api-experimental.md` i think

docs/docs/api-experimental.md

gcarleo · 2022-02-16T18:08:27Z

good to squash and merge for me

@imi-hub

This is an implementation of discrete fermionic degrees of freedom by @imi-hub and myself. It contains the hilbert space and an operator. The operator handles the minus signs coming from the exchange symmetry, while the hilbert space stores occupation numbers only. This follows e.g. the way qiskit and openfermion would implement things. For the operator, we follow the implementation of openfermion and added an 'from_openfermion' function to create operators. This allows us to use all their hamiltonians, such as Fermi-Hubbard. Co-authored-by: Imelda Romero <imelda.romero@epfl.ch> Co-authored-by: Filippo Vicentini <filippovicentini@gmail.com>

jwnys requested review from PhilipVinc and gcarleo January 31, 2022 12:32

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Implementation of fermionic hilbert and operator #1090

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Implementation of fermionic hilbert and operator #1090

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