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content/qspin/bose-hubbard-model/hamiltonian-and-ground-state-data.md
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$$ | ||
-t ( \sum_{\langle i, j\rangle} \hat{b}^\dagger_i\hat{b}_j + h.c.) + U \sum_i \hat{n}_{i}\hat{n}_{i} | ||
$$ | ||
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Hamiltonians for the spin systems (under the Jordan-Wigner transformation for the Fermi Hubbard model and [Binary Bosonic mapping](https://arxiv.org/abs/2105.12563) for the Bose Hubbard Model). | ||
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| Name | Type | Description | | ||
|-----------------|-------------------|----------------------------------------------------------------| | ||
| `hamiltonian` | list[`Hamiltonian`] | Hamiltonian of the system in the Pauli basis | | ||
| `ground_energies` | `numpy.ndarray` | Ground state energies of each configuration of the spin system | | ||
| `ground_states` | `numpy.ndarray` | Ground state of each configuration of the spin system | |
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11 changes: 11 additions & 0 deletions
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content/qspin/fermi-hubbard-model/hamiltonian-and-ground-state-data.md
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$$ | ||
-t(\sum_{\langle i, j\rangle, \sigma} \hat{c}^\dagger_i\hat{c}_j + h.c.) + U \sum_i \hat{n}_{i\uparrow} \hat{n}_{i\downarrow} | ||
$$ | ||
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Hamiltonians for the spin systems (under the Jordan-Wigner transformation for the Fermi Hubbard model and [Binary Bosonic mapping](https://arxiv.org/abs/2105.12563) for the Bose Hubbard Model). | ||
|
||
| Name | Type | Description | | ||
|-----------------|-------------------|----------------------------------------------------------------| | ||
| `hamiltonian` | list[`Hamiltonian`] | Hamiltonian of the system in the Pauli basis | | ||
| `ground_energies` | `numpy.ndarray` | Ground state energies of each configuration of the spin system | | ||
| `ground_states` | `numpy.ndarray` | Ground state of each configuration of the spin system | |
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content/qspin/transverse-field-ising-model/hamiltonian-and-ground-state-data.md
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$$ | ||
J\sum_{\langle i,j\rangle} \sigma_i^z\sigma_j^z + h\sum_i \sigma_i^x | ||
$$ | ||
|
||
Hamiltonians for the spin systems (under the Jordan-Wigner transformation for the Fermi Hubbard model and [Binary Bosonic mapping](https://arxiv.org/abs/2105.12563) for the Bose Hubbard Model). | ||
|
||
| Name | Type | Description | | ||
|-----------------|-------------------|----------------------------------------------------------------| | ||
| `hamiltonian` | list[`Hamiltonian`] | Hamiltonian of the system in the Pauli basis | | ||
| `ground_energies` | `numpy.ndarray` | Ground state energies of each configuration of the spin system | | ||
| `ground_states` | `numpy.ndarray` | Ground state of each configuration of the spin system | |
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11 changes: 11 additions & 0 deletions
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content/qspin/xxz-heisenberg-model/hamiltonian-and-ground-state-data.md
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$$ | ||
J_{xy}\sum_{\langle i,j\rangle}(\sigma_i^x\sigma_j^x+\sigma_i^y\sigma_j^y) + J_z\sum_{\langle i,j\rangle} \sigma_i^z \sigma_j^z | ||
$$ | ||
|
||
Hamiltonians for the spin systems (under the Jordan-Wigner transformation for the Fermi Hubbard model and [Binary Bosonic mapping](https://arxiv.org/abs/2105.12563) for the Bose Hubbard Model). | ||
|
||
| Name | Type | Description | | ||
|-----------------|-------------------|----------------------------------------------------------------| | ||
| `hamiltonian` | list[`Hamiltonian`] | Hamiltonian of the system in the Pauli basis | | ||
| `ground_energies` | `numpy.ndarray` | Ground state energies of each configuration of the spin system | | ||
| `ground_states` | `numpy.ndarray` | Ground state of each configuration of the spin system | |
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