13,385 research outputs found
Spatial and spin symmetry breaking in semidefinite-programming-based Hartree-Fock theory
The Hartree-Fock problem was recently recast as a semidefinite optimization
over the space of rank-constrained two-body reduced-density matrices (RDMs)
[Phys. Rev. A 89, 010502(R) (2014)]. This formulation of the problem transfers
the non-convexity of the Hartree-Fock energy functional to the rank constraint
on the two-body RDM. We consider an equivalent optimization over the space of
positive semidefinite one-electron RDMs (1-RDMs) that retains the non-convexity
of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble
-representability conditions, and ensemble spin-state conditions may be
imposed as well. The spin-state conditions place additional linear and
nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several
molecular systems and explore its spatial (point group) and spin ( and
) symmetry breaking properties. When imposing and symmetry but
relaxing point group symmetry, the procedure often locates
spatial-symmetry-broken solutions that are difficult to identify using standard
algorithms. For example, the RDM-based approach yields a smooth,
spatial-symmetry-broken potential energy curve for the well-known Be--H
insertion pathway. We also demonstrate numerically that, upon relaxation of
and symmetry constraints, the RDM-based approach is equivalent to
real-valued generalized Hartree-Fock theory.Comment: 9 pages, 6 figure
On the Adler-Bell-Jackiw anomaly in a Horava-Lifshitz-like QED
We show the absence of the ABJ anomaly for the Horava-Lifshitz-like QED with
any even . Besides of this, we study the graph contributing to the ABJ
anomaly at non-zero temperature and extend the Fujikawa's methodology of
studying the integral measure for our model.Comment: 9 pages, version accepted to EP
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