We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
Error in fermi-hubbard example
Hello, there.

It seems that the definition of create and annihilation operators are defined reversely in fermi-hubbard model, and results are wrong. [link](https://github.com/netket/netket/blob/26372e3527ae12861cc7953c24654614e8679d87/Examples/Fermions/fermi_hubbard.py#L25C1-L26)

--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `Examples/Fermions/fermi_hubbard.py`
Content:
```
1 import netket as nk
2 import numpy as np
3 import matplotlib.pyplot as plt
4 import json
5 
6 from netket import experimental as nkx
7 
8 L = 2  # take a 2x2 lattice
9 D = 2
10 t = 1  # tunneling/hopping
11 U = 0.01  # coulomb
12 
13 # create the graph our fermions can hop on
14 g = nk.graph.Hypercube(length=L, n_dim=D, pbc=True)
15 n_sites = g.n_nodes
16 
17 # create a hilbert space with 2 up and 2 down spins
18 hi = nkx.hilbert.SpinOrbitalFermions(n_sites, s=1 / 2, n_fermions=(2, 2))
19 
20 
21 # create an operator representing fermi hubbard interactions
22 # -t (i^ j + h.c.) + U (i^ i j^ j)
23 # we will create a helper function to abbreviate the creation, destruction and number operators
24 # each operator has a site and spin projection (sz) in order to find the right position in the hilbert space samples
25 def c(site, sz):
26     return nkx.operator.fermion.create(hi, site, sz=sz)
27 
28 
29 def cdag(site, sz):
30     return nkx.operator.fermion.destroy(hi, site, sz=sz)
31 
32 
33 def nc(site, sz):
34     return nkx.operator.fermion.number(hi, site, sz=sz)
35 
36 
37 up = +1 / 2
38 down = -1 / 2
39 ham = 0.0
40 for sz in (up, down):
41     for u, v in g.edges():
42         ham += -t * cdag(u, sz) * c(v, sz) - t * cdag(v, sz) * c(u, sz)
43 for u in g.nodes():
44     ham += U * nc(u, up) * nc(u, down)
45 
46 print("Hamiltonian =", ham.operator_string())
47 
48 # metropolis exchange moves fermions around according to a graph
49 # the physical graph has LxL vertices, but the computational basis defined by the
50 # hilbert space contains (2s+1)*L*L occupation numbers
51 # by taking a disjoint copy of the lattice, we can
52 # move the fermions around independently for both spins
53 # and therefore conserve the number of fermions with up and down spin
54 
55 # g.n_nodes == L*L --> disj_graph == 2*L*L
56 disj_graph = nk.graph.disjoint_union(g, g)
57 sa = nk.sampler.MetropolisExchange(hi, graph=disj_graph, n_chains=16)
58 
59 # since the hilbert basis is a set of occupation numbers, we can take a general RBM
60 # we take complex parameters, since it learns sign structures more easily, and for even fermion number, the wave function might be complex
61 ma = nk.models.RBM(alpha=1, param_dtype=complex, use_visible_bias=False)
62 vs = nk.vqs.MCState(sa, ma, n_discard_per_chain=100, n_samples=512)
63 
64 # we will use sgd with Stochastic Reconfiguration
65 opt = nk.optimizer.Sgd(learning_rate=0.01)
66 sr = nk.optimizer.SR(diag_shift=0.1)
67 
68 gs = nk.driver.VMC(ham, opt, variational_state=vs, preconditioner=sr)
69 
70 # now run the optimization
71 # first step will take longer in order to compile
72 exp_name = "fermions_test"
73 gs.run(500, out=exp_name)
74 
75 ############## plot #################
76 
77 ed_energies = np.linalg.eigvalsh(ham.to_dense())
78 
79 with open(f"{exp_name}.log", "r") as f:
80     data = json.load(f)
81 
82 x = data["Energy"]["iters"]
83 y = data["Energy"]["Mean"]["real"]
84 
85 # plot the energy levels
86 plt.axhline(ed_energies[0], color="red", label="E0")
87 for e in ed_energies[1:]:
88     plt.axhline(e, color="black")
89 plt.plot(x, y, color="red", label="VMC")
90 plt.xlabel("step")
91 plt.ylabel("E")
92 plt.show()
93
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/Examples/Fermions/fermi_hubbard.py b/Examples/Fermions/fermi_hubbard.py
--- a/Examples/Fermions/fermi_hubbard.py
+++ b/Examples/Fermions/fermi_hubbard.py
@@ -23,11 +23,11 @@
 # we will create a helper function to abbreviate the creation, destruction and number operators
 # each operator has a site and spin projection (sz) in order to find the right position in the hilbert space samples
 def c(site, sz):
-    return nkx.operator.fermion.create(hi, site, sz=sz)
+    return nkx.operator.fermion.destroy(hi, site, sz=sz)
 
 
 def cdag(site, sz):
-    return nkx.operator.fermion.destroy(hi, site, sz=sz)
+    return nkx.operator.fermion.create(hi, site, sz=sz)
 
 
 def nc(site, sz):

{"golden_diff": "diff --git a/Examples/Fermions/fermi_hubbard.py b/Examples/Fermions/fermi_hubbard.py\n--- a/Examples/Fermions/fermi_hubbard.py\n+++ b/Examples/Fermions/fermi_hubbard.py\n@@ -23,11 +23,11 @@\n # we will create a helper function to abbreviate the creation, destruction and number operators\n # each operator has a site and spin projection (sz) in order to find the right position in the hilbert space samples\n def c(site, sz):\n-    return nkx.operator.fermion.create(hi, site, sz=sz)\n+    return nkx.operator.fermion.destroy(hi, site, sz=sz)\n \n \n def cdag(site, sz):\n-    return nkx.operator.fermion.destroy(hi, site, sz=sz)\n+    return nkx.operator.fermion.create(hi, site, sz=sz)\n \n \n def nc(site, sz):\n", "issue": "Error in fermi-hubbard example\nHello, there.\r\n\r\nIt seems that the definition of create and annihilation operators are defined reversely in fermi-hubbard model, and results are wrong. [link](https://github.com/netket/netket/blob/26372e3527ae12861cc7953c24654614e8679d87/Examples/Fermions/fermi_hubbard.py#L25C1-L26)\n", "before_files": [{"content": "import netket as nk\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport json\n\nfrom netket import experimental as nkx\n\nL = 2  # take a 2x2 lattice\nD = 2\nt = 1  # tunneling/hopping\nU = 0.01  # coulomb\n\n# create the graph our fermions can hop on\ng = nk.graph.Hypercube(length=L, n_dim=D, pbc=True)\nn_sites = g.n_nodes\n\n# create a hilbert space with 2 up and 2 down spins\nhi = nkx.hilbert.SpinOrbitalFermions(n_sites, s=1 / 2, n_fermions=(2, 2))\n\n\n# create an operator representing fermi hubbard interactions\n# -t (i^ j + h.c.) + U (i^ i j^ j)\n# we will create a helper function to abbreviate the creation, destruction and number operators\n# each operator has a site and spin projection (sz) in order to find the right position in the hilbert space samples\ndef c(site, sz):\n    return nkx.operator.fermion.create(hi, site, sz=sz)\n\n\ndef cdag(site, sz):\n    return nkx.operator.fermion.destroy(hi, site, sz=sz)\n\n\ndef nc(site, sz):\n    return nkx.operator.fermion.number(hi, site, sz=sz)\n\n\nup = +1 / 2\ndown = -1 / 2\nham = 0.0\nfor sz in (up, down):\n    for u, v in g.edges():\n        ham += -t * cdag(u, sz) * c(v, sz) - t * cdag(v, sz) * c(u, sz)\nfor u in g.nodes():\n    ham += U * nc(u, up) * nc(u, down)\n\nprint(\"Hamiltonian =\", ham.operator_string())\n\n# metropolis exchange moves fermions around according to a graph\n# the physical graph has LxL vertices, but the computational basis defined by the\n# hilbert space contains (2s+1)*L*L occupation numbers\n# by taking a disjoint copy of the lattice, we can\n# move the fermions around independently for both spins\n# and therefore conserve the number of fermions with up and down spin\n\n# g.n_nodes == L*L --> disj_graph == 2*L*L\ndisj_graph = nk.graph.disjoint_union(g, g)\nsa = nk.sampler.MetropolisExchange(hi, graph=disj_graph, n_chains=16)\n\n# since the hilbert basis is a set of occupation numbers, we can take a general RBM\n# we take complex parameters, since it learns sign structures more easily, and for even fermion number, the wave function might be complex\nma = nk.models.RBM(alpha=1, param_dtype=complex, use_visible_bias=False)\nvs = nk.vqs.MCState(sa, ma, n_discard_per_chain=100, n_samples=512)\n\n# we will use sgd with Stochastic Reconfiguration\nopt = nk.optimizer.Sgd(learning_rate=0.01)\nsr = nk.optimizer.SR(diag_shift=0.1)\n\ngs = nk.driver.VMC(ham, opt, variational_state=vs, preconditioner=sr)\n\n# now run the optimization\n# first step will take longer in order to compile\nexp_name = \"fermions_test\"\ngs.run(500, out=exp_name)\n\n############## plot #################\n\ned_energies = np.linalg.eigvalsh(ham.to_dense())\n\nwith open(f\"{exp_name}.log\", \"r\") as f:\n    data = json.load(f)\n\nx = data[\"Energy\"][\"iters\"]\ny = data[\"Energy\"][\"Mean\"][\"real\"]\n\n# plot the energy levels\nplt.axhline(ed_energies[0], color=\"red\", label=\"E0\")\nfor e in ed_energies[1:]:\n    plt.axhline(e, color=\"black\")\nplt.plot(x, y, color=\"red\", label=\"VMC\")\nplt.xlabel(\"step\")\nplt.ylabel(\"E\")\nplt.show()\n", "path": "Examples/Fermions/fermi_hubbard.py"}], "after_files": [{"content": "import netket as nk\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport json\n\nfrom netket import experimental as nkx\n\nL = 2  # take a 2x2 lattice\nD = 2\nt = 1  # tunneling/hopping\nU = 0.01  # coulomb\n\n# create the graph our fermions can hop on\ng = nk.graph.Hypercube(length=L, n_dim=D, pbc=True)\nn_sites = g.n_nodes\n\n# create a hilbert space with 2 up and 2 down spins\nhi = nkx.hilbert.SpinOrbitalFermions(n_sites, s=1 / 2, n_fermions=(2, 2))\n\n\n# create an operator representing fermi hubbard interactions\n# -t (i^ j + h.c.) + U (i^ i j^ j)\n# we will create a helper function to abbreviate the creation, destruction and number operators\n# each operator has a site and spin projection (sz) in order to find the right position in the hilbert space samples\ndef c(site, sz):\n    return nkx.operator.fermion.destroy(hi, site, sz=sz)\n\n\ndef cdag(site, sz):\n    return nkx.operator.fermion.create(hi, site, sz=sz)\n\n\ndef nc(site, sz):\n    return nkx.operator.fermion.number(hi, site, sz=sz)\n\n\nup = +1 / 2\ndown = -1 / 2\nham = 0.0\nfor sz in (up, down):\n    for u, v in g.edges():\n        ham += -t * cdag(u, sz) * c(v, sz) - t * cdag(v, sz) * c(u, sz)\nfor u in g.nodes():\n    ham += U * nc(u, up) * nc(u, down)\n\nprint(\"Hamiltonian =\", ham.operator_string())\n\n# metropolis exchange moves fermions around according to a graph\n# the physical graph has LxL vertices, but the computational basis defined by the\n# hilbert space contains (2s+1)*L*L occupation numbers\n# by taking a disjoint copy of the lattice, we can\n# move the fermions around independently for both spins\n# and therefore conserve the number of fermions with up and down spin\n\n# g.n_nodes == L*L --> disj_graph == 2*L*L\ndisj_graph = nk.graph.disjoint_union(g, g)\nsa = nk.sampler.MetropolisExchange(hi, graph=disj_graph, n_chains=16)\n\n# since the hilbert basis is a set of occupation numbers, we can take a general RBM\n# we take complex parameters, since it learns sign structures more easily, and for even fermion number, the wave function might be complex\nma = nk.models.RBM(alpha=1, param_dtype=complex, use_visible_bias=False)\nvs = nk.vqs.MCState(sa, ma, n_discard_per_chain=100, n_samples=512)\n\n# we will use sgd with Stochastic Reconfiguration\nopt = nk.optimizer.Sgd(learning_rate=0.01)\nsr = nk.optimizer.SR(diag_shift=0.1)\n\ngs = nk.driver.VMC(ham, opt, variational_state=vs, preconditioner=sr)\n\n# now run the optimization\n# first step will take longer in order to compile\nexp_name = \"fermions_test\"\ngs.run(500, out=exp_name)\n\n############## plot #################\n\ned_energies = np.linalg.eigvalsh(ham.to_dense())\n\nwith open(f\"{exp_name}.log\", \"r\") as f:\n    data = json.load(f)\n\nx = data[\"Energy\"][\"iters\"]\ny = data[\"Energy\"][\"Mean\"][\"real\"]\n\n# plot the energy levels\nplt.axhline(ed_energies[0], color=\"red\", label=\"E0\")\nfor e in ed_energies[1:]:\n    plt.axhline(e, color=\"black\")\nplt.plot(x, y, color=\"red\", label=\"VMC\")\nplt.xlabel(\"step\")\nplt.ylabel(\"E\")\nplt.show()\n", "path": "Examples/Fermions/fermi_hubbard.py"}]}