How to build spin hamiltonians #1230
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| # spin-down particle. The Hamiltonian describing this model has two components: the kinetic energy | ||
| # component which is parameterized by a hopping parameter and the potential energy component | ||
| # parameterized by the on-site interaction strength. The Fermi-Hubbard Hamiltonian can then be | ||
| # constructed in PennyLane by passing the hoping and interaction parameters to the fermi_hubbard |
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even if the link doesn't work now, I would add this
| # constructed in PennyLane by passing the hoping and interaction parameters to the fermi_hubbard | |
| # constructed in PennyLane by passing the hoping and interaction parameters to the :func:`fermi_hubbard <pennylane.spin.fermi_hubbard>` |
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the same for all other functions. Another option is to put ``function name``, so that it is not seen in plain text
| # | ||
| # PennyLane has a range of functions for constructing spin model Hamiltonians with minimal input | ||
| # data needed from the user. Let’s look at the | ||
| # `Fermi-Hubbard <https://pennylane.ai/datasets/qspin/fermi-hubbard-model>`__ model as an example. |
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I was confused by your pointing to the dataset as I thought we were using it but they are different things
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| ###################################################################### | ||
| # Similarity, a broad range of other well-investigated spin model Hamiltonians can be constructed | ||
| # with the dedicated functions available in the spin module, by just providing the lattice |
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I don't know if we can link it now but it would be good to add a link here to the spin module
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If we can't link it, we can maybe provide a list of spin-Hamiltonians we can construct.
| # Hamiltonian templates | ||
| # --------------------- | ||
| # | ||
| # PennyLane has a range of functions for constructing spin model Hamiltonians with minimal input |
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Can you mention a couple of different Hamiltonian examples?
| # examples of both methods. First we use generate_lattice to construct a square lattice containing 9 | ||
| # sites which are all connected to their nearest neighbor. | ||
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| lattice = qml.spin.lattice._generate_lattice('square', [3, 3]) |
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curious about why this is a private function
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It will become public in a WIP PR.
| # manually is more flexible while generate_lattice only works for some predefined lattice shapes. | ||
| # | ||
| # Now that we have the lattice, we can use its attributes, e.g., edges and vertices, to construct | ||
| # our transverse field Ising model Hamiltonian. We just need to define the coupling and onsite |
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You might remember the reader that these are J and h
| # nodes and the unit cell translation vector and then define the number of unit cells in each | ||
| # direction. | ||
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| nodes = [[0.5, 0.5 / 3 ** 0.5], [1, 1 / 3 ** 0.5]] |
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Not sure I understand what the nodes are here
| ###################################################################### | ||
| # Let's plot the lattice to see how it looks like. | ||
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| plot(Lattice(n_cells, vectors, nodes), figsize=(5, 3)) |
| hamiltonian = qml.spin.fermi_hubbard("cubic", [3, 3, 3], t, u) | ||
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| ###################################################################### | ||
| # Similarity, a broad range of other well-investigated spin model Hamiltonians can be constructed |
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| # Similarity, a broad range of other well-investigated spin model Hamiltonians can be constructed | |
| # Similarly, a broad range of other well-investigated spin model Hamiltonians can be constructed |
| # The Hamiltonian template functions are great and simple tools for someone who just wants to build | ||
| # a Hamiltonian quickly. However, PennyLane offers intuitive tools that can be used to construct | ||
| # spin Hamiltonians manually which are very handy for building customized Hamiltonians. Let’s learn | ||
| # how to use this tools by constructing the Hamiltonian for the |
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| # how to use this tools by constructing the Hamiltonian for the | |
| # how to use these tools by constructing the Hamiltonian for the |
soranjh
changed the title
| # spin-down particle. The Hamiltonian describing this model has two components: the kinetic energy | ||
| # component which is parameterized by a hopping parameter and the potential energy component | ||
| # parameterized by the on-site interaction strength. The Fermi-Hubbard Hamiltonian can then be | ||
| # constructed in PennyLane by passing the hoping and interaction parameters to the fermi_hubbard |
There was a problem hiding this comment.
| # constructed in PennyLane by passing the hoping and interaction parameters to the fermi_hubbard | |
| # constructed in PennyLane by passing the hopping and interaction parameters to the fermi_hubbard |
| n = [2] | ||
| t = 0.2 | ||
| u = 0.3 |
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Shall we add comments here to say which term describes what parameter or rename the parameters? This might get confusing as we don't provide the equation here.
| # The fermi_hubbard function is general enough to go beyond the simple “chain” model and construct | ||
| # the Hamiltonian for a wide range of two-dimensional and three-dimensional lattice shapes. For | ||
| # those cases, we need to provide the number of sites in each direction of the lattice. We can | ||
| # construct the Hamiltonian for a cubic lattice with 3 sites on each direction as |
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| # construct the Hamiltonian for a cubic lattice with 3 sites on each direction as | |
| # construct the Hamiltonian for a cubic lattice with 3 sites in each direction as |
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| ###################################################################### | ||
| # Similarity, a broad range of other well-investigated spin model Hamiltonians can be constructed | ||
| # with the dedicated functions available in the spin module, by just providing the lattice |
There was a problem hiding this comment.
If we can't link it, we can maybe provide a list of spin-Hamiltonians we can construct.
| # spin Hamiltonians manually which are very handy for building customized Hamiltonians. Let’s learn | ||
| # how to use this tools by constructing the Hamiltonian for the | ||
| # `transverse field Ising <https://pennylane.ai/datasets/qspin/transverse-field-ising-model>`__ | ||
| # model on a two-dimension lattice. |
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| # model on a two-dimension lattice. | |
| # model on a two-dimensional lattice. |
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| ###################################################################### | ||
| # This gives us the same lattice as we created with generate_lattice but constructing the lattice | ||
| # manually is more flexible while generate_lattice only works for some predefined lattice shapes. |
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We can link the generate_lattice function here, so that a reader can see which pre-defined shapes are available.
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| ###################################################################### | ||
| # In this example we just used the in-built attributes of the lattice we created without further | ||
| # customising them. The lattice can be constructed in a very flexible way that allows constructing |
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| # customising them. The lattice can be constructed in a very flexible way that allows constructing | |
| # customising them. The lattice can be constructed in a more flexible way that allows constructing |
| n_cells = [3, 3] | ||
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| ###################################################################### | ||
| # Let's plot the lattice to see how it looks like. |
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| # Let's plot the lattice to see how it looks like. | |
| # Let's plot the lattice to see how it looks. |
| # See how we can easily and intuitively construct the Kitaev model Hamiltonian with the tools in | ||
| # these tools. You can compare the constructed Hamiltonian with the template we already have for | ||
| # the Kitaev model and verify that the Hamiltonians are the same. |
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| # See how we can easily and intuitively construct the Kitaev model Hamiltonian with the tools in | |
| # these tools. You can compare the constructed Hamiltonian with the template we already have for | |
| # the Kitaev model and verify that the Hamiltonians are the same. | |
| # See how we can easily and intuitively construct the Kitaev model Hamiltonian with the tools available in the | |
| # spin module. You can compare the constructed Hamiltonian with the template we already have for | |
| # the Kitaev model and verify that the Hamiltonians are the same. |
| # Hamiltonians. Here we learned how to use these tools to construct pre-defined Hamiltonian | ||
| # templates, such as the Fermi-Hubbard model Hamiltonian, and use the Lattice object to construct | ||
| # more advanced and customised models such as the Kitaev honeycomb Hamiltonian. The versatility of | ||
| # the new spin functions and classes allows constructing any new spin model Hamiltonian intuitively. |
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| # the new spin functions and classes allows constructing any new spin model Hamiltonian intuitively. | |
| # the new spin functions and classes allows construction of any new spin model Hamiltonian intuitively. |
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Title:
How to build spin hamiltonians [sc-74419]
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This how-to explains the features added to the
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