mSASS part 2 - the d^1 configuration in an octahedral field with spin-orbit coupling—Wolfram Documentation Not Found - Wolfram Cloud
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mSASS part 2 - the d1 configuration in an octahedral field with spin-orbit coupling

mSASS part 2 - the d1 configuration in an octahedral field with spin-orbit coupling

Expected level splittingEigenvalues of the mSASS Hamiltonian
The mSASS Hamiltonian
The tutorial shows the construction of the mSASS-Hamiltonian for a d1 configuration in octahedral fields with spin-orbit interaction. It is a continuation of part 1 - d1 configuration in an octahedral field. More information can be found in the following reference:
Expected level splitting
The octahedral symmetry is described by the point group O. Under spin-orbit coupling, a d-orbital splits into two orbitals with total angular momenta j=3/2 and j=5/2. First, we compute the character system of the SU(2) representations with j=3/2 and j=5/2 and analyze their decomposition into irreducible representations of O.
GTInstallGroup
Installs point and space groups
GTCharacterTable
Comutes the character table
GTAngularMomentumChars
Gives the characters of representations of O(3) or SU(2)
GTIrep
Computes the decomposition of a reducible representation into irreducible representations of a group
Install the double group of O by specifying the option GORepresentation .
Compute the character table.
Compute the splitting of the j = 3/2 multiplet in octahedral symmetry.
Compute the splitting of the j = 5/2 multiplet in octahedral symmetry.
The mSASS Hamiltonian
GTAngularMomentumRep
Computes representation matrices for the irreducible representations of O(3) or SU(2)
GClebschGordanSum
Constructs the Clebsch-Gordan sum of two representations
Compute the representation matrices of SU (2) , for both, j=3/2 and j=5/2.
Construct super representation in terms of the Clebsch-Gordan sum of the j=3/2 and j=5/2 representation.
An example matrix, with the j=3/2 block in the upper left part and the j=5/2 block in the lower right part.
Generate a generic 10x10 Hamiltonian matrix.
Project the symmetry invariant part.
Solve for the symmetry invariant terms.
Construct the final Hermitian Hamiltonain.
Eigenvalues of the mSASS Hamiltonian
Compute the eigenvalues
Simplify by redefining the terms.
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