Modern Physics Letters A

Topological ordered phases are gapped states of matter that are characterized by non-local entanglement in their ground state wave functions instead of a local order parameter. In this paper, we review some of the basic results on the entanglement structure of topologically ordered phases. In particular, we focus on the notion and uses of "topological entanglement entropy" in two and higher dimensions, and also briefly review the relation between entanglement spectrum and the spectrum of the physical edge states for chiral topological states. Furthermore, we discuss a curvature expansion for the entanglement entropy which sharpens the nonlocality of topological entanglement entropy.

Shapere and Wilczek recently found some singular Lagrangian systems which spontaneously breaks time translation symmetry. The common feature of their models is that the energy functions are multi-valued in terms of the canonical phase space variables and the symmetry breaking ground states are all located at the brunching point singularities. By enlarging the phase space and making use of Dirac's theory on constrained Hamiltonian systems, we present the Hamiltonian description of some of the models discussed by Shapere and Wilczek and found that both the multi-valuedness and the brunching point singularities can be avoided, while the spontaneous breaking of time translation becomes more transparent. It is also shown that the breaking of time translation is always accompanied by the breaking of time reversal.

The action for a (3+1)-dimensional particle in very special relativity (VSR) is studied. It is proved that massless particles only travel in effective (2+1)-dimensional spacetime. It is remarkable that this action can be written as an action for a relativistic particle in a background gauge field and it is shown that this field causes the dimensional reduction. A new symmetry for this system is found. Furthermore, a general action with restored Lorentz symmetry is proposed for this system. It is shown that this new action contains VSR and two-time physics.

Binding energies and their differences are investigated to evaluate the two-neutron separation energies (S_2n), the two-proton separation energies (S_2p) and the average proton–neutron interaction strengths (δV_pn) of neutron-rich Sr, Zr and Mo isotopes in the mass region A = 86–110, including even–even nuclei. Calculations were performed using the Hartree–Fock–Bogoliubov (HFB) method with different Skyrme force parametrizations. The obtained results are discussed and compared with the results of experimental and relativistic mean-field theory (RMFT).

We study the structure of weight modules V with restrictions neither on the dimension nor on the base field, over split Lie algebras L. We show that if L is perfect and V satisfies LV = V and , then

It is pointed out (not for the first time) that the minimal Standard Model, without additional gauge-singlet right-handed neutrinos or isotriplet Higgs fields, allows for nonvanishing neutrino masses and mixing. The required interaction term is non-renormalizable and violates B-L conservation. The ultimate explanation of this interaction term may or may not rely on grand unification.