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Journal of Yancheng Institute of Technology

The Transformation Between Hubbard Operators and Pauli Matrices

WU Jun-fang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Aiming at the transformation of Hamiltonian from Pauli matrices to Hubbard operators, the authors use the unity and orthogonal of Hubbard operators to give the transforming formula of Pauli matrices and Hubbard operators, by which, they realize the change from Pauli matrices to Hubbard operators.The result has been obtained that the Hamiltonian expressed by Hubbard operators of the spin-ladder model.

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The Transform Between Hubbard Operators and Pauli Matrices

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Aim The Hamiltonian is transformed from Pauli matrices to Hubbard operators. Method we use the unity and orthogonal of Hubbard operators to give the transforming formula of Pauli matrices and Hubbard operators, by using these transforming formula we realize the change from Pauli matrices to Hubbard operators. Result we get the Hamiltonian expressed by Hubbard operators of the spin-ladder model. Conclusion We use the example to realize the transform between Hubbard operators and Pauli matrices.

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Aiming at the transformation of Hamiltonian from Pauli matrices to Hubbard operators, the authors use the unity and orthogonal of Hubbard operators to give the transforming formula of Pauli matrices and Hubbard operators, by which, they realize the change from Pauli matrices to Hubbard operators.The result has been obtained that the Hamiltonian expressed by Hubbard operators of the spin-ladder model.
In quantum mechanics, there are some classical bases which are generalized to higher dimensional matrices. So, it is useful to express their corresponding operators using the Dirac Bra and Ket. In this paper, to express the corresponding operators we review the Kronecker-Pauli matrices and how to construct them for an N-dimensional system, with N a prime integer, N>2. Then, we give the expression of the Kronecker-Pauli operators and show that their matrices with respect to the standard basis fulfill the conditions to form a Kronecker-Pauli matrices.
In quantum mechanics, classical matrix bases such as the Pauli matrices are often generalized to higher dimensions. So, it is useful to express their corresponding operators using the Dirac Bra and Ket. In this paper, to express the corresponding operators we review the Kronecker-Pauli matrices and how to construct them for an N-dimensional system, with N a prime integer, N>2. Then, we give the expression of the Kronecker-Pauli operators and show that their matrices with respect to the standard basis fulfill the conditions to form a set of Kronecker-Pauli matrices. Relationship between the Kronecker-Pauli operators and the Weyl operators has been studied.
In quantum mechanics, classical matrix bases such as the Pauli matrices are often generalized to higher dimensions. So, it is useful to express their corresponding operators using the Dirac Bra and Ket. In this paper, to express the corresponding operators we review the Kronecker-Pauli matrices and how to construct them for an N-dimensional system, with N a prime integer, N>2. Then, we give the expression of the Kronecker-Pauli operators and show that their matrices with respect to the standard basis fulfill the conditions to form a set of Kronecker-Pauli matrices.