Globally symmetric spinor condensates in free space are argued not to support stable topological defects in either two or three dimensions. In the latter case, however, we show that a topological Skyrmion can be stabilized by forcing it to adopt certain density profiles. A sufficient condition for the existence of Skyrmion solutions in three dimensions is formulated and illustrated in simple examples. Our results pertain to Bose-Einstein condensation in 87Rb.
In numerical simulations, spontaneously broken symmetry is often detected by computing twopoint correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and so when it is small, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetry breaking field, and then measure the induced local order parameter infinitely far from the pinning center. The method is tested here at length for the Hubbard model on honeycomb lattice, within the realm of the projective auxiliary field quantum Monte Carlo algorithm. With our enhanced resolution we find a direct and continuous quantum phase transition between the semi-metallic and the insulating antiferromagnetic states with increase of the interaction. The single particle gap in units of the Hubbard U tracks the staggered magnetization. An excellent data collapse is obtained by finite size scaling, with the values of the critical exponents in accord with the Gross-Neveu universality class of the transition.
The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated by the lattice is D_2 x U_c(1) x (time reversal), where D_2 is the dihedral group, and U_c(1) is a subgroup of the SU_c(2) "chiral" group of the non-interacting Lagrangian, that represents translations in Dirac language. The Lagrangian describing spinless particles respecting this symmetry is parameterized by six independent coupling constants. We show how first imposing the rotational, then Lorentz, and finally chiral symmetry to the quartic terms, in conjunction with the Fierz transformations, eventually reduces the set of couplings to just two, in the "maximally symmetric" local interacting theory. We identify the two critical points in such a Lorentz and chirally symmetric theory as describing metal-insulator transitions into the states with either time-reversal or chiral symmetry being broken. In the site-localized limit of the interacting Hamiltonian the low-energy theory describes the continuous transitions into the insulator with either a finite Haldane's (circulating currents) or Semenoff's (staggered density) masses, both in the universality class of the Gross-Neveu model. The picture of the metal-insulator transition on a honeycomb lattice emerges at which the residue of the quasiparticle pole at the metallic and the mass-gap in the insulating phase both vanish continuously as the critical point is approached. We argue that the Fermi velocity is non-critical as a consequence of the dynamical exponent being fixed to unity by the emergent Lorentz invariance. Effects of long-range interaction and the critical behavior of specific heat and conductivity are discussed.Comment: 16 revtex pages, 4 figures; typos corrected, new and updated references; published versio
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