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Full docs for Hamiltonian

Types

These Term types may be added together freely. Multiplication with scalars works as expected. You can only impose spatial information (via multiplication with a vector or matrix respective of the type of term) once! You can only add together compatible terms in terms of spatial structure.

SpinModels.X — Function
X(J=1)

Represents a $\sigma_x^{(i)}$ term. Multiply with a vector h to get the term $\sum_i h_i \sigma_x^{(i)} .$

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SpinModels.Y — Function
Y(J=1)

Represents a $\sigma_y^{(i)}$ term. Multiply with a vector h to get the term $\sum_i h_i \sigma_y^{(i)} .$

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SpinModels.Z — Function
Z(J=1)

Represents a $\sigma_z^{(i)}$ term. Multiply with a vector h to get the term $\sum_i h_i \sigma_z^{(i)} .$

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SpinModels.XX — Function
XX(J=1)

Represents a $\sigma_x^{(i)} \sigma_x^{(j)}$ term. Multiply with a matrix J to get the term $\sum_{i\neq j} J_{ij} \sigma_x^{(i)} \sigma_x^{(j)} .$

Note

Two-body terms do 'double-counting' of the couplings meaning the sum runs over i,j independently and not i < j.

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SpinModels.YY — Function
YY(J=1)

Represents a $\sigma_y^{(i)} \sigma_y^{(j)}$ term. Multiply with a matrix J to get the term $\sum_{i\neq j} J_{ij} \sigma_y^{(i)} \sigma_y^{(j)} .$

Note

Two-body terms do 'double-counting' of the couplings meaning the sum runs over i,j independently and not i < j.

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SpinModels.ZZ — Function
ZZ(J=1)

Represents a $\sigma_z^{(i)} \sigma_z^{(j)}$ term. Multiply with a matrix J to get the term $\sum_{i\neq j} J_{ij} \sigma_z^{(i)} \sigma_z^{(j)} .$

Note

Two-body terms do 'double-counting' of the couplings meaning the sum runs over i,j independently and not i < j.

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SpinModels.Hopp — Function
Hopp(J=1)

Represents a $\sigma_+^{(i)} \sigma_-^{(j)} + \mathrm{h.c.}$ term. Multiply with a matrix J to get the term $\sum_{i\neq j} J_{ij} \sigma_+^{(i)} \sigma_-^{(j)} + \mathrm{h.c.} .$

Note

Two-body terms do 'double-counting' of the couplings meaning the sum runs over i,j independently and not i < j.

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Functions

SpinModels.nspins — Method
nspins(term)
nspins(sum_of_terms)

Return the number of spins in the underlying geometry if that information was already provided.

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