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arXiv:1808.03025 · Physical Review A

Topological bosonic states on ribbons of a honeycomb lattice

Yi‐Ping Wang, Xingchuan Zhu, Kefei Zou, Shengyuan A. Yang, Huaiming Guo

Published Oct 15, 2018• 3 citations
arXivHTMLPDF

Abstract

The topological properties of hardcore bosons on ribbons of honeycomb lattice are studied using quantum Monte Carlo simulations. We map out a rich phase diagram with the superfluid and insulator phases at various fillings. Particularly, it is revealed that the insulator state at half filling is a topological bosonic state, which is characterized by a nontrivial Berry phase and a pair of end states. We provide an intuitive picture to understand this topological bosonic insulator state by showing that it can be adiabatically mapped to a topological fermionic model. It is also shown that the topological end states are robust against weak interactions beyond the hardcore repulsion. Our results can be simulated by using bosonic cold atoms trapped in designed optical lattices.

DOI
10.1103/physreva.98.043617

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The topological properties of hardcore bosons on ribbons of honeycomb lattice are studied using quantum Monte Carlo simulations. We map out a rich phase diagram with the superfluid and insulator phases at various fillings. Particularly, it is revealed that the insulator state at half filling is a topological bosonic state, which is characterized by a nontrivial Berry phase and a pair of end states. We provide an intuitive picture to understand this topological bosonic insulator state by showing that it can be adiabatically mapped to a topological fermionic model. It is also shown that the topological end states are robust against weak interactions beyond the hardcore repulsion. Our results can be simulated by using bosonic cold atoms trapped in designed optical lattices.
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Quantum Monte Carlo (QMC) simulation has uncovered nonzero Berry curvature and bosonic edge states in the hardcore-Bose-Hubbard model on the gapped honeycomb lattice. The competition between the chemical potential and staggered onsite potential leads to an interesting quantum phase diagram comprising the superfluid phase, Mott insulator, and charge density wave insulator. In this paper, we present a semiclassical perspective of this system by mapping to a spin-1/2 quantum XY model. We give an explicit analytical origin of the quantum phase diagram, the Berry curvatures, and the edge states using semiclassical approximations. We find very good agreement between the semiclassical analyses and the QMC results. Our results show that the topological properties of the hardcore-Bose-Hubbard model are the same as those of magnon in the corresponding quantum spin system. Our results are applicable to systems of ultracold bosonic atoms trapped in honeycomb optical lattices.
We study the phases of hard-core bosons on a two-dimensional periodic honeycomb lattice in the presence of an on-site potential with alternating sign along the different y-layers of the lattice. Using quantum Monte Carlo simulations supported by analytical calculations, we identify a weak topological insulator, characterized by a zero Chern number but non-zero Berry phase, which is manifested at either density 1/4 or 3/4, as determined by the potential pattern. Additionally, a charge-density-wave insulator is observed at 1/2-filling, whereas the phase diagram at intermediate densities is occupied by a superfluid phase. The weak topological insulator is further shown to be robust against any amount of nearest-neighbor repulsion, as well as weak next-nearest-neighbor repulsion. The experimental realization of our model is feasible in an optical lattice setup.
This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-1/2 quantum XY model with a next-nearest-neighbour Dzyaloshinsky–Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, and thermal and spin Nernst conductivities. Because of the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological properties as those in quantum spin systems. These results are important in the study of magnetic excitations in quantum magnets and they are also useful for understanding the control of ultracold bosonic quantum gases in honeycomb optical lattices, which is experimentally accessible.
We study hard-core bosons on the honeycomb lattice in the presence of anisotropic nearest-neighbor repulsive interactions. Using a quantum Monte Carlo (QMC) technique, we extract the phase diagram of the model in terms of the filling and the anisotropy. At half-filling we find a dimer insulator phase near maximum anisotropy that is characterized by a finite topological entanglement entropy ln(2)/2ln(2)/2ln(2)/2, indicative of a fractional quantum Hall state for bosons. We identify the presence of edge states and derive a QMC-based method to extract and verify their chirality. Remarkably, this phase arises in the absence of magnetic flux and without explicit lattice frustration.
We study hard-core bosons on the honeycomb lattice subjected to anisotropic nearest-neighbor hopping along with anisotropic nearest-neighbor repulsion, using a quantum Monte Carlo technique. At half filling, we find a transition from strong topological interacting order to weak topological interacting order as a function of the hopping anisotropy. The strong topological phase is characterized by a finite topological entanglement entropy, while the weak topological order is identified with a nontrivial value of the bipartite entanglement entropy. Some of the order parameters and their derivatives demonstrate abrupt changes when varying the parameters controlling the lattice anisotropies, thus revealing the nature of this topological interacting phase transition.