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arXiv:1509.03037 · Physical Review A

π Berry phase and topological excitation in interacting boson-fermion mixtures

Huaiming Guo

Published Sep 28, 2015• 3 citations
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Abstract

The topological property of a boson-fermion mixture in a one-dimensional optical superlattice is studied and the topological insulating phase of an interacting boson-fermion mixture characterized by a nontrivial Berry phase is identified. The single-particle and boson-fermion exchanging excitation spectrums are calculated and we identify the boson-fermion exchanging excitation as the gapless topological excitation in the topological phase of the mixture. The different kinds of excitations are explained explicitly from the competition among the bulk gap, the on-site boson-boson, and boson-fermion interactions. The Hamiltonian studied has been partly realized in the state-of-art cold atom experiments, and the results are very relevant to the experiments.

DOI
10.1103/physreva.92.033625

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The topological property of a boson-fermion mixture in a one-dimensional optical superlattice is studied and the topological insulating phase of an interacting boson-fermion mixture characterized by a nontrivial Berry phase is identified. The single-particle and boson-fermion exchanging excitation spectrums are calculated and we identify the boson-fermion exchanging excitation as the gapless topological excitation in the topological phase of the mixture. The different kinds of excitations are explained explicitly from the competition among the bulk gap, the on-site boson-boson, and boson-fermion interactions. The Hamiltonian studied has been partly realized in the state-of-art cold atom experiments, and the results are very relevant to the experiments.
We investigate topological phase transitions driven by interaction and identify a topological Mott insulator state in one-dimensional fermionic optical superlattices through a numerical density-matrix renormalization-group method. Remarkably, the low-energy edge excitations change from spin-1/2 fermionic single-particle modes to spin-1 bosonic collective modes across the phase transition. Due to spin-charge separation, the low-energy theory is governed by an effective spin superexchange model, whereas the charge degree of freedom is fully gapped out. Such topological Mott state can be characterized by a spin Chern number and gapless magnon modes protected by a finite spin gap. The proposed experimental setup is simple and may pave the way for the experimental observation of exotic topological Mott states.
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We study a one-dimensional (1D) interacting topological model by means of the exact diagonalization method. The topological properties are first 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 nontrivial phase into a trivial one while the attractive interaction can drive a trivial phase into a nontrivial 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 the large-UUU limit and provide an additional understanding of the numerical results. These results could be realized experimentally using cold atoms trapped in the 1D optical lattice.
We study the topological properties of an extended Bose-Hubbard model with cyclically modulated hopping and on-site potential parameters, which can be realized with ultracold bosonic atoms in a one-dimensional optical superlattice. We show that the interacting bosonic chain at half filling and in the deep Mott insulating regime can simulate bosonic Chern insulators with a topological phase diagram similar to that of the Haldane model of noninteracting fermions. Furthermore, we explore the topological properties of the ground state by calculating the many-body Chern number, the quasiparticle energy spectrum with gapless edge modes, the topological pumping of the interacting bosons, and the topological phase transition from normal (trivial) to topological Mott insulators. We also present the global phase diagram of the many-body ground state, which contains a superfluid phase and two Mott insulating phases with trivial (a zero Chern number) and nontrivial topologies (a nonzero Chern number), respectively.
Superfluid-insulator transitions in a one-dimensional mixture of two-color fermions and scalar bosons are studied within the framework of the Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for repulsive intraspecies interactions and attractive or repulsive interspecies couplings. In addition to the trivial Mott insulator phases, we report the emergence of nontrivial insulator phases that depend on the sign of the boson-fermion interaction. These nontrivial insulator phases satisfy the conditions ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\rho}}_{F}=n$ and ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}\frac{1}{2}{\ensuremath{\rho}}_{F}=n$, with the plus (minus) sign for repulsive (attractive) interactions and nnn an integer. Far from fermionic half filling, the boson-fermion interaction drives a gapless-gapped transition in the spin sector. Our findings could be observed experimentally in state-of-the-art cold-atom setups.
We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor $\ensuremath{\nu}=1$ and in the presence of the on-site Hubbard interaction, we find no sign of the existence of the bosonic topological phase, which is in contrast to the fermionic case. Instead by studying the momentum distribution and the condensate fraction we find a superfluid to Mott-insulator transition driven by the Hubbard interaction. At the filling factor $\ensuremath{\nu}=1/3$ and in the presence of longer-ranged interactions, we identify the bosonic fractional topological phase whose ground states are characterized by a threefold degeneracy and a quantized total Berry phase, which is very similar to the fermionic case. Finally we discuss the reason for the different behaviors of hard-core bosons at different filling factors by mapping them to spinless fermions. Our results can be realized in cold-atom experiments.