All functions in Melt:

• are Non-invasive: They will not change Mathematica’s native functionality.
• Are Input > Output: You input some parameters and it spits out a result.
• Work with normal or sparse arrays They do not use “quantum objects,” just standard matrices and vectors.
• Numerics & symbolics: Whenever it makes sense, the functions will accept symbolic input just as well as numeric input.

There are 6 main types of functions in Melt:

There are also various other functions implemented. But these 6 categories should give you an idea of the basic functionality.

“Load” functions for setting up Pauli matrices, bosonic/fermionic operators &c.

Load functions load into memory a set of desired operators. For instance:

This overrides the symbols $\sigma_0, \sigma_x, \ldots$ with the Pauli matrices.

<aside> <img src="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/1ce1352b-9ab7-4b06-bac4-a65fd493831e/Transparent.png" alt="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/1ce1352b-9ab7-4b06-bac4-a65fd493831e/Transparent.png" width="40px" /> I personally run LoadPauliMatrices[] automatically every time I initialize Mathematica. That way, the Pauli matrices are always at hand.

</aside>

For a spin chain, one can use

The argument is the number of sites in the chain.

• “$\sigma$” quantities are still the $2\times 2$ Pauli matrices.