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arXiv:1304.3958 · Physical Review A

Hard-core bosons in one-dimensional interacting topological bands

Huaiming Guo

Published Nov 30, 2012• 12 citations
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Abstract

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.

DOI
10.1103/physreva.86.055604

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We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor \ensuremathν=1\ensuremath{\nu}=1\ensuremathν=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 \ensuremathν=1/3\ensuremath{\nu}=1/3\ensuremathν=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.
We show the existence of the fractional topological phase (FTP) in a one-dimensional interacting fermion model using exact diagonalization, in which the noninteracting part has flat bands with nontrivial topology. In the presence of the nearest-neighboring interaction V1{V}_{1}V1​, the FTP at filling factor $\ensuremath{\nu}=1/3$ appears. It is characterized by the threefold degeneracy and the quantized total Berry phase of the ground states. The FTP is destroyed by a next-nearest-neighboring interaction V2{V}_{2}V2​, and the phase diagrams in the (V1,V2)({V}_{1},{V}_{2})(V1​,V2​) plane are determined. We also present a physical picture of the phase and discuss its existence in the nearly flat band. 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.
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There has been a growing interest in realizing topologically nontrivial states of matter in band insulators, where a quantum Hall effect can appear as an intrinsic property of the band structure. While ongoing progress is under way with a number of directions, the possibility of realizing novel interaction-generated topological phases, without the requirement of a nontrivial invariant encoded in single-particle wave function or band structure, can significantly extend the class of topological materials and is thus of great importance. Here, we show an interaction-driven topological phase emerging in an extended Bose-Hubbard model on a kagome lattice, where the noninteracting band structure is topological trivial with zero Berry curvature in the Brillouin zone. By means of an unbiased state-of-the-art density-matrix renormalization group technique, we identify that the ground state in a broad parameter region is equivalent to a bosonic fractional quantum Hall Laughlin state, based on the characterization of universal properties including ground-state degeneracy, edge excitations, and anyonic quasiparticle statistics. Our work paves a way to finding an interaction-induced topological phase at the phase boundary of conventionally ordered solid phases.
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Recent theoretical works have demonstrated various robust Abelian and non-Abelian fractional topological phases in lattice models with topological flat bands carrying Chern number C=1C=1C=1. Here we study hard-core bosons and interacting fermions in a three-band triangular-lattice model with the lowest topological flat band of Chern number C=2C=2C=2. We find convincing numerical evidence of bosonic fractional quantum Hall effect at the $\ensuremath{\nu}=1/3$ filling characterized by threefold quasidegeneracy of ground states on a torus, a fractional Chern number for each ground state, a robust spectrum gap, and a gap in quasihole excitation spectrum. We also observe numerical evidence of a robust fermionic fractional quantum Hall effect for spinless fermions at the $\ensuremath{\nu}=1/5$ filling with short-range interactions.
We study a model for two-species hard-core bosons in one dimension. In this model, the same-species bosons have a hard-core condition at the same site, while different-species bosons are allowed to occupy the same site with a local interaction U . At half-filling, by Jordan-Wigner transformation, the model can be exactly mapped to a fermionic Hubbard model. Due to this correspondence, the phase transition from superfluid ( U = 0) to Mott insulator ( U > 0) can be explained by simple one-band theory at half-filling. By using an exact diagonalization method adopting a modified Lanczos method, we obtain the ground states as a function of U for the lattice size upto L = 16. We calculate directional current-current correlation functions in this model, which indicate that there are some remaining counter-flow in the Mott insulating region ( U > 0) and co-flow in the charge-density-wave region ( U <0) for the finite lattices.