Ground-state Competition of Two-Component Bosons in Optical Lattice near a Feshbach Resonance

We investigate the ground state properties of an equal mixture of two species of bosons in its Mott-insulator phase at a filling factor two per site. We identify one type of spin triplet-singlet transition through the competition of ground state. When the on-site interaction is weak ($U<U_c$) the two particles prefer to stay in the lowest band and with weak tunnelling between neighboring sites the system is mapped into an effective spin-1 ferromagnetic exchange Hamiltonian. When the interaction is tuned by a Feshbach resonance to be large enough ($U>U_c$), higher band will be populated. Due to the orbital coupling term $S^+S^-$ in the Hamiltonian, the two atoms in different orbits on a site would form an on-site singlet. For a non-SU(2)-symmetric model, easy-axis or easy-plane ferromagnetic spin exchange models may be realized corresponding to phase separation or counter-flow superfluidity, respectively.Comment: Final version in PR

Magnetism of Cold Fermionic Atoms on p-Band of an Optical Lattice

We carry out \textit{ab initio} study of ground state phase diagram of spin-1/2 cold fermionic atoms within two-fold degenerate $p$-band of an anisotropic optical lattice. Using the Gutzwiller variational approach, we show that a robust ferromagnetic phase exists for a vast range of band fillings and interacting strengths. The ground state crosses over from spin density wave state to spin-1 Neel state at half filling. Additional harmonic trap will induce spatial separation of varies phases. We also discuss several relevant observable consequences and detection methods. Experimental test of the results reported here may shed some light on the long-standing issue of itinerant ferromagnetism.Comment: 5 pages, 4 figure

Predicting the ‘Unpredictable’ General Anti-Avoidance Rule (GAAR) in EU Tax Law

General Anti-Avoidance Rule (GAAR) is a type of rule designed to combat the tax-avoidance scenarios that in a legal form lawfully but aims to circumvent the legal consequences. GAAR is necessary for a tax system to address unexpected innovative tax avoidance scenarios. In the field of tax law, GAAR has been criticized for being too abstract and thus harmful to legal certainty. In the context of EU integration, the concept of GAAR has been developed and elaborated by Court of Justice of European Union as well as secondary laws, but there are quite a few different formulations. In the existing literature, it is established that, there are the subject test and the objective test cumulatively in the GAAR, which examines the taxpayers’ subjective intension and the objective economic reality. As to the relation between these two tests, scholars have established the theory that, the formulation and the context of the subjective test is actually influenced by the tax rule involved (that is, the purpose of the norm being circumvented). This paper will revisit GAARs in the EU tax law and present that, the theory of GAAR based on the purpose of the violated tax norm is indeed supported by latest case law of CJEU as well new Directives. Furthermore, the intention of the norm reconciles the subject test and the objective test. In this regard, the unpredictability of ‘GAAR’ actually has become more predictable