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arXiv:2204.01514 · Physical review. B./Physical review. B

Integer quantum Hall effect of two-component hard-core bosons in a topological triangular lattice

Tian-Sheng Zeng

Published Jun 27, 2022• 3 citations
arXivHTMLPDF

Abstract

We study the many-body ground states of two-component hard-core bosons in topological triangular-lattice models. Utilizing exact diagonalization and density-matrix renormalization group calculations, we demonstrate that at commensurate two-thirds filling per lattice site, a two-component bosonic integer quantum Hall (BIQH) effect emerges with the associated $\mathbf{K}=(\begin{array}{cc}0& 1\\ 1& 0\end{array})$ matrix under strong intercomponent Hubbard repulsion. The topological nature is further elucidated by (i) a unique ground state degeneracy with a robust spectrum gap, (ii) a quantized topological Chern number matrix $\mathbf{C}={\mathbf{K}}^{\ensuremath{-}1}$, and (iii) two counterpropagating edge branches. Moreover, with increasing nearest-neighbor repulsions, the ground state undergoes a first-order transition from a BIQH liquid to a commensurate solid order.

DOI
10.1103/physrevb.105.235140

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We study the many-body ground states of two-component hard-core bosons in topological triangular-lattice models. Utilizing exact diagonalization and density-matrix renormalization group calculations, we demonstrate that at commensurate two-thirds filling per lattice site, a two-component bosonic integer quantum Hall (BIQH) effect emerges with the associated K=(0110)\mathbf{K}=(\begin{array}{cc}0& 1\\ 1& 0\end{array})K=(01​10​) matrix under strong intercomponent Hubbard repulsion. The topological nature is further elucidated by (i) a unique ground state degeneracy with a robust spectrum gap, (ii) a quantized topological Chern number matrix C=K\ensuremath−1\mathbf{C}={\mathbf{K}}^{\ensuremath{-}1}C=K\ensuremath−1, and (iii) two counterpropagating edge branches. Moreover, with increasing nearest-neighbor repulsions, the ground state undergoes a first-order transition from a BIQH liquid to a commensurate solid order.
Quantum Hall effects with multicomponent internal degrees of freedom facilitate the playground of novel emergent topological orders. Here, we explore the correlated topological phases of two-component hardcore bosons at a total filling factor ν = 2/5 in topological lattice models under the interplay of intracomponent and intercomponent repulsions. We give the numerical demonstration of the emergence of Halperin (441) fractional quantum Hall effect based on exact diagonalization and density-matrix renormalization group methods. We elucidate its topological features including the degeneracy of the ground state, fractionally quantized topological Chern number matrix and chiral edge modes.
We study the many-body ground states of three-component quantum particles in two prototypical topological lattice models under strong intercomponent and intracomponent repulsions. At band filling $\ensuremath{\nu}=3/4$ for hard-core bosons, we demonstrate the emergence of the three-component fractional quantum Hall (FQH) effect characterized by the K\mathbf{K}K matrix, through an exact diagonalization study of fourfold quasidegenerate ground states with a robust spectrum gap and the combined density-matrix renormalization group calculation of fractional drag charge pumping. Further, we formulate the topological characterization of FQH states of three-component Bose-Fermi mixtures at various fillings by the K\mathbf{K}K matrix. Finally, we discuss the possible generalization of our approach to identify non-Abelian three-component spin-singlet FQH states.
We study interacting two-component hard-core bosons on a square lattice for which, in the presence of staggered magnetic flux, its ground state is a bosonic integer quantum Hall (BIQH) state. By using a coupled-wire bosonization approach, we show analytically that this model exhibits a BIQH state at total charge half filling associated with a symmetry-protected topological phase under U(1)\text{U}(1)U(1) charge conservation. These theoretical expectations are verified, using the infinite density matrix renormalization group method, by providing numerical evidence for (i) a quantized Hall conductance ${\ensuremath{\sigma}}_{xy}=\ifmmode\pm\else\textpm\fi{}2$, and (ii) two counterpropagating gapless edge modes. Our model is a bosonic cousin of the fermionic Haldane model and serves as an additional case of analogy between bosonic and fermionic quantum Hall states.
Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of strongly correlated Bose-Fermi mixtures classified by the K=(m11n)\mathbf{K}=\left(\begin{array}{cc}m& 1\\ 1& n\end{array}\right)K=(m1​1n​) matrix (even mmm for boson and odd nnn for fermion), using topological flat band models. Utilizing the state-of-the-art exact diagonalization and density-matrix renormalization group methods, we build up the topological characterization based on three inherent aspects: (i) topological $(mn\ensuremath{-}1)$-fold ground-state degeneracy equivalent to the determinant of the K\mathbf{K}K matrix; (ii) fractionally quantized topological Chern number matrix equivalent to the inverse of the K\mathbf{K}K matrix; and (iii) two parallel-propagating chiral edge branches with level counting 1,2,5,10 consistent with the conformal field theory description.
We study a bosonic model with correlated hopping on a honeycomb lattice, and show that its ground state is a bosonic integer quantum Hall (BIQH) phase, a prominent example of a symmetry-protected topological (SPT) phase. By using the infinite density matrix renormalization group method, we establish the existence of the BIQH phase by providing clear numerical evidence: (i) a quantized Hall conductance with |σ_{xy}|=2, (ii) two counterpropagating gapless edge modes. Our simple model is an example of a novel class of systems that can stabilize SPT phases protected by a continuous symmetry on lattices and opens up new possibilities for the experimental realization of these exotic phases.
The Halperin $({m}^{\ensuremath{'}},m,n)$ fractional quantum Hall effects of two-component quantum particles are studied in topological checkerboard lattice models. Here for $m\ensuremath{\ne}{m}^{\ensuremath{'}}$, we demonstrate the emergence of fractional quantum hall effects with the associated K=(m+211m)\mathbf{K}=\left(\begin{array}{cc}m+2& 1\\ 1& m\end{array}\right)K=(m+21​1m​) matrix (even m=2m=2m=2 for boson and odd m=3m=3m=3 for fermion) in the presence of both strong intercomponent and intracomponent repulsions. Through exact diagonalization and density-matrix renormalization group calculations, we elucidate their topological fractionalizations, including (i) the $det|\mathbf{K}|=({m}^{2}+2m\ensuremath{-}1)$-fold ground-state degeneracies and (ii) fractionally quantized topological Chern number matrix $\mathbf{C}={\mathbf{K}}^{\ensuremath{-}1}$. Our flat band model provides a paradigmatic example of a microscopic Hamiltonian featuring fractional quantum Hall effect with partial spinpolarization.