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
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.
