No abstract

No abstract

It is well known that the pristine bulk of an interacting one dimensional (1D) system in Tomonaga-Luttinger liquid (TLL) phase shows power law suppression of quasi-particle tunneling amplitude for all values of TLL parameter g, in the zero energy limit. We perform a density matrix renormalization group (DMRG) study of a fully symmetric Y junction of TLL wires and observe an anomalous enhancement of the tunneling density of states (TDOS) in the vicinity of the junction for both (a) interacting hardcore bosons case and (b) interacting fermions case, when g > 1. We also observe suppression of TDOS for g < 1 for both bosonic and fermionic case. We find that the TDOS enhancements follow different power laws for bosonic and fermionic cases which suggests that these represent distinct fixed points owing to statistical correlations which play an important role at the Y junction. Analysis of static conductance for the junction indicates that the fermionic fixed point for 3 > g > 1 resembles the mysterious M-fixed point of Y junction predicted by Oshikawa, Chamon, and Affleck [

No abstract

We examine the topological properties of a one-dimensional (1D) chain of fermions with spin-orbit coupling, Zeeman field, and attractive Hubbard interaction by numerically computing the pair binding energy, excitation gap, and susceptibility to local perturbations by density matrix renormalization group. Such a system can in principle be realized in a 1D optical lattice. We find that, in the presence of spatial interfaces introduced by a smooth parabolic potential, the variation of the pair binding energy and the excitation gap with the system size indicate an exponentially vanishing fermion parity gap and topological ground state degeneracy in the thermodynamic limit, consistent with recent works. However, the susceptibility of the ground state degeneracy to local perturbations indicate that the vanishing of the fermion parity gap in this number conserving system scales as a power-law in system size. We compare the present system with the more familiar system of an Ising antiferromagnet in the presence of a transverse field realized with Rydberg atoms, and argue that the degeneracy of this conventional symmetry-breaking system is identical to the 1D chain of fermions considered. Therefore, the degeneracy properties of the 1D chain of fermions cannot be attributed to topology.