The deconfined quantum critical point (DQCP) between the N\'eel and valence bond solid order was originally proposed in spin systems with a local Hamiltonian. In last few years analogs of DQCPs nonlocal interactions have been explored, which can lead to rich possibilities. either arise from an instantaneous long-range interaction Hamiltonian, or gapless modes that reside one higher spatial dime...

We prove Timmesfeld’s conjecture that special abstract rank one groups are quasisimple. We show that in a special Moufang set the root groups are characterized on the one hand by being regular and normal in the point stabilizer, and on the other hand a normal transitive nilpotent subgroup of the point stabilizer is a root group. We prove that if a root group of a special Moufang set contains an...

We examine the relation between twisted versions of the extended supersymmetric gauge theories and supersymmetric orbifold lattices. In particular, for the N = 4 SYM in d = 4, we show that the continuum limit of orbifold lattice reproduces the twist introduced by Marcus, and the examples at lower dimensions are usually Blau-Thompson type. The orbifold lattice point group symmetry is a subgroup ...

In this paper we extend the method of canonical form for congruence bilinear forms to give classification some subclasses 7-dimensional nilpotent Leibniz algebras. Odd-nilpotent algebras are defined as that its even dimensional ideals in lower central series all zero and complex odd-nilpotent with one Leib ideal is obtained by applying aforementioned method.