Topological phase in one-dimensional interacting fermion system

We study a one-dimensional interacting topological model by means of exact diagonalization method. The topological properties are firstly examined with the existence of the edge states at half-filling. We find that the topological phases are not only robust to small repulsive interactions but also are stabilized by small attractive interactions, and also finite repulsive interaction can drive a topological non-trivial phase into a trivial one while the attractive interaction can drive a trivial phase into a non-trivial one. Next we calculate the Berry phase and parity of the bulk system and find that they are equivalent in characterizing the topological phases. With them we obtain the critical interaction strengths and construct part of the phase diagram in the parameters space. Finally we discuss the effective Hamiltonian at large-U limit and provide additional understanding of the numerical results. Our these results could be realized experimentally using cold atoms trapped in the 1D optical lattice.Comment: 7 pages, 5 figures; revised version, references added, Accepted for publication in Physical Review

Observational Constraints on Secret Neutrino Interactions from Big Bang Nucleosynthesis

We investigate possible interactions between neutrinos and massive scalar bosons via $g^{}_{\phi} \overline{\nu} \nu \phi$ (or massive vector bosons via $g^{}_V \overline{\nu} \gamma^\mu \nu V^{}_\mu$) and explore the allowed parameter space of the coupling constant $g^{}_{\phi}$ (or $g^{}_V$) and the scalar (or vector) boson mass $m^{}_\phi$ (or $m^{}_V$) by requiring that these secret neutrino interactions (SNIs) should not spoil the success of Big Bang nucleosynthesis (BBN). Incorporating the SNIs into the evolution of the early Universe in the BBN era, we numerically solve the Boltzmann equations and compare the predictions for the abundances of light elements with observations. It turns out that the constraint on $g^{}_{\phi}$ and $m^{}_\phi$ in the scalar-boson case is rather weak, due to a small number of degrees of freedom. However, in the vector-boson case, the most stringent bound on the coupling $g^{}_V \lesssim 6\times 10^{-10}$ at $95~\%$ confidence level is obtained for $m^{}_V \simeq 1~{\rm MeV}$, while the bound becomes much weaker $g^{}_V \lesssim 8\times 10^{-6}$ for smaller masses $m^{}_V \lesssim 10^{-4}~{\rm MeV}$. Moreover, we discuss in some detail how the SNIs affect the cosmological evolution and the abundances of the lightest elements.Comment: 18 pages, 5 figure

Fractional topological phase in one-dimensional flatbands with nontrivial topology

We show the existence of the fractional topological phase (FTP) in a one-dimensional interacting fermion model using exact diagonalization, in which the non-interacting part has flatbands with nontrivial topology. In the presence of the nearest-neighbouring interaction $V_{1}$, the FTP at filling factor $\nu =1/3$ appears. It is characterized by the three-fold degeneracy and the quantized total Berry phase of the ground-states. The FTP is destroyed by a next-nearest-neighbouring interaction $V_{2}$ and the phase diagrams in the $(V_{1},V_{2})$ plane is determined. We also present a physical picture of the phase and discuss its existence in the nearly flatband. Within the picture, we argue that the FTP at other filling factors can be generated by introducing proper interactions. The present study contributes to a systematic understanding of the FTPs and can be realized in cold-atom experiments.Comment: 5 pages, 5 figures. To appear in Phys. Rev.

Complete phase diagram and topological properties of interacting bosons in one-dimensional superlattices

The interacting bosons in one-dimensional inversion-symmetric superlattices are investigated from the topological aspect. The complete phase diagram is obtained by an atomic-limit analysis and quantum Monte Carlo simulations and comprises three kinds of phases: superfluid, persisted charge-density-wave and Mott insulators, and emergent insulators in the presence of nearest-neighbor hoppings. We find that all emergent insulators are topological, which are characterized by the Berry phase $\pi$ and a pair of degenerate in-gap boundary states. The mechanism of the topological bosonic insulators is qualitatively discussed and the ones with higher fillings can be understood as a $\frac{1}{3}$-filling topological phase on a background of trivial charge-density-wave or Mott insulators.Comment: 6 pages, 8 figures. Accelpted for publication in Phys. Rev.