We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid.Turning on a large easy-plane spin anis...We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid.Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid.Both phases have full spin gaps and exhibit power-law superconducting pair correlation.The Cooper pair symmetry is singlet dxy in the non-trivial phase and triplet Sz? 0 in the trivial phase.The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary,and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned.As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes.We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.展开更多
A novel polymer-bound 1,2-diol, 3-polystyrylsulfonyl-1,2-propanediol (6) had been prepared by the reaction of sodium polystyrylsulfinate with allyl bromide, followed by oxidation and. hydrolysis or directly with 3-chl...A novel polymer-bound 1,2-diol, 3-polystyrylsulfonyl-1,2-propanediol (6) had been prepared by the reaction of sodium polystyrylsulfinate with allyl bromide, followed by oxidation and. hydrolysis or directly with 3-chloro-1,2-propanediol in the presence of a phase transfer catalyst, n-tetrabutylammonium iodide. The capacity of resin 6 for terephthaidehyde reached 1.43 mmol/g. The aldehydic groups attached to polymer 6 reacted with hydroxylamine hydrochloride or reduced by sodium borohydride giving p-formylbenzaldoxime (yield: 89%)and p-formyl-benzalcohol (yield: 734%), respectively. The high yields of these polymer-supported reactions showed that the polymer 6 possessed the effective isolation of its reactive sites.展开更多
基金supported by the U.S.Department of Energy,Office of Science,Office of Advanced Scientific Computing Research,Scientific Discovery through Advanced Computing(SciDAC)program
文摘We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid.Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid.Both phases have full spin gaps and exhibit power-law superconducting pair correlation.The Cooper pair symmetry is singlet dxy in the non-trivial phase and triplet Sz? 0 in the trivial phase.The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary,and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned.As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes.We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.
基金The project is supported by the National Natural Science Foundation of China.
文摘A novel polymer-bound 1,2-diol, 3-polystyrylsulfonyl-1,2-propanediol (6) had been prepared by the reaction of sodium polystyrylsulfinate with allyl bromide, followed by oxidation and. hydrolysis or directly with 3-chloro-1,2-propanediol in the presence of a phase transfer catalyst, n-tetrabutylammonium iodide. The capacity of resin 6 for terephthaidehyde reached 1.43 mmol/g. The aldehydic groups attached to polymer 6 reacted with hydroxylamine hydrochloride or reduced by sodium borohydride giving p-formylbenzaldoxime (yield: 89%)and p-formyl-benzalcohol (yield: 734%), respectively. The high yields of these polymer-supported reactions showed that the polymer 6 possessed the effective isolation of its reactive sites.
