Track papers across labs, topics, and trends.
Search papers, labs, and topics across Lattice.
This study clarifies the operator associated with a proposed conserved quantity for the many-electron Dirac-Coulomb Hamiltonian, revealing it as a component of a pseudospin linked to Kramers pairs. The authors demonstrate that the angular-momentum algebra of this pseudospin reproduces the previously reported integer eigenvalue spectrum and provides closed-form eigenvectors. However, they challenge the validity of the proposed quantum number, showing that it does not commute with the Hamiltonian and is therefore not a legitimate quantum number.
The supposed conserved quantum number for the many-electron Dirac-Coulomb Hamiltonian is fundamentally flawed, as it fails to commute with the Hamiltonian.
The square of a sum of single-electron time reversals has been proposed as a conserved quantity with an integer eigenvalue spectrum for the many-electron Dirac-Coulomb Hamiltonian [Phys. Rev. A 94, 052104 (2016)], and its expectation value is in use as a diagnostic of Kramers contamination. This work identifies the operator behind the construction, a component of a pseudospin attached to the chosen Kramers pairs, whose angular-momentum algebra reproduces the reported spectrum and yields the eigenvectors in closed form. The label $k$ entering the proposed quantum number $-k^2$ is twice the magnitude of a pseudospin projection onto an axis fixed by the basis and changes when the Kramers pairs are rephased. The commutation with the Hamiltonian is unfounded, and the proposed quantum number does not stand.