A linear combination of products of Majorana operators.

A system of N fermionic modes can be described using 2N Majorana operators \(\gamma_1, \ldots, \gamma_{2N}\) as an alternative to using N fermionic annihilation operators. The algebra of Majorana operators amounts to the relation

\[ \{\gamma_i, \gamma_j\} = \gamma_i \gamma_j + \gamma_j \gamma_i = 2 \delta_{ij} \]

Note that this implies \(\gamma_i^2 = 1\).

The MajoranaOperator class stores a linear combination of products of Majorana operators. Each product is represented as a tuple of integers representing the indices of the operators. As an example, MajoranaOperator((2, 3, 5), -1.5) initializes an operator with a single term which represents the operator \(-1.5 \gamma_2 \gamma_3 \gamma_5\). MajoranaOperators can be added, subtracted, multiplied, and divided by scalars. They can be compared for approximate numerical equality using ==.

term Tuple[int]

The indices of a Majorana operator term to start off with

coefficient complex

The coefficient of the term

terms A dictionary from term, represented by a tuple of integers, to the coefficient of the term in the linear combination.



View source

Test commutation with another MajoranaOperator


View source

Initialize a MajoranaOperator from a terms dictionary.

terms A dictionary from Majorana term to coefficient


View source

Change to a basis of new Majorana operators.

The input to this method is a real orthogonal matrix \(O\). It returns a new MajoranaOperator which is equivalent to the old one but rewritten in terms of a new basis of Majorana operators. Let the original Majorana operators be denoted by \(\gamma_i\) and the new operators be denoted by \(\tilde{\gamma_i}\). Then they are related by the equation

\[ \tilde{\gamma_i} = \sum_j O_{ij} \gamma_j. \]

transformation_matrix A real orthogonal matrix representing the basis transformation.

The rotated operator.


View source


View source

Approximate numerical equality.


View source


View source

Return self!=value.


View source


View source


View source


View source


View source