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arXiv:1304.5716 · Physical Review Letters

Integer Quantum Hall State in Two-Component Bose Gases in a Synthetic Magnetic Field

Shunsuke Furukawa, Masahito Ueda

Published Aug 26, 2013• 75 citations
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Abstract

We study two-component (or pseudospin-1/2) Bose gases in a strong synthetic magnetic field. Using exact diagonalization, we show that a bosonic analog of an integer quantum Hall state with no intrinsic topological order appears at the total filling factor ν=1+1 when the strengths of intracomponent and intercomponent interactions are comparable with each other. This provides a prime example of a symmetry-protected topological phase in a controlled setting of quantum gases. The real-space entanglement spectrum of this state is found to be comprised of counterpropagating chiral modes consistent with the edge theory derived from an effective Chern-Simons theory.

DOI
10.1103/physrevlett.111.090401

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We study two-component (or pseudospin-1/2) Bose gases in a strong synthetic magnetic field. Using exact diagonalization, we show that a bosonic analog of an integer quantum Hall state with no intrinsic topological order appears at the total filling factor ν=1+1 when the strengths of intracomponent and intercomponent interactions are comparable with each other. This provides a prime example of a symmetry-protected topological phase in a controlled setting of quantum gases. The real-space entanglement spectrum of this state is found to be comprised of counterpropagating chiral modes consistent with the edge theory derived from an effective Chern-Simons theory.
We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-12\frac{1}{2}21​) Bose gases in a high synthetic magnetic field in the space of the total filling factor and the ratio of the intercomponent coupling ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ to the intracomponent one g>0g>0g>0. Using exact diagonalization, we find that when the intercomponent coupling is attractive (${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}<0$), the product states of a pair of nearly uncorrelated quantum Hall states are remarkably robust and persist even when $|{g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}|$ is close to ggg. This contrasts with the case of an intercomponent repulsion, where a variety of spin-singlet quantum Hall states with high intercomponent entanglement emerge for ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}\ensuremath{\approx}g$. We interpret this marked dependence on the sign of ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ in light of pseudopotentials on a sphere, and also explain recent numerical results in two-component Bose gases in mutually antiparallel magnetic fields where a qualitatively opposite dependence on the sign of ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ is found. Our results thus unveil an intriguing connection between multicomponent quantum Hall systems and quantum spin Hall systems in minimal setups.
We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-12\frac{1}{2}21​) Bose gases in mutually antiparallel synthetic magnetic fields in the space of the total filling factor and the ratio of the intercomponent coupling ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ to the intracomponent coupling g>0g>0g>0. This time-reversal-invariant setting represents a bosonic analog of spin Hall systems. Using exact diagonalization, we find that (fractional) quantum spin Hall states composed of a pair of nearly independent quantum Hall states are remarkably robust and persist for ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ up to as large as ggg. For ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}=\ensuremath{-}g$, we find the exact many-body ground state in which particles in different spin states form pairs. This gives the exact critical line beyond which the system collapses in the thermodynamic limit.
The recent production of synthetic magnetic fields acting on electroneutral particles, such as atoms or photons, has boosted interest in the quantum Hall physics of bosons. Adding pseudospin 1/2 to the bosons greatly enriches the scenario, as it allows them to form an interacting integer quantum Hall (IQH) phase with no fermionic counterpart. Here we show that, for a small two-component Bose gas on a disk, the complete strongly correlated regime, extending from the integer phase at filling factor $\ensuremath{\nu}=2$ to the Halperin phase at filling factor $\ensuremath{\nu}=2/3$, is well described by composite fermionization of the bosons. Moreover we study the edge excitations of the IQH state, which, in agreement with expectations from topological field theory, are found to consist of forward-moving charge excitations and backward-moving spin excitations. Finally, we demonstrate how pair-correlation functions allow one to experimentally distinguish the IQH state from competing states, such as non-Abelian spin singlet (NASS) states.
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 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 $\mathbf{C}={\mathbf{K}}^{\ensuremath{-}1}$, 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.
In two dimensions strongly interacting bosons in a magnetic field can form an integer quantum Hall state. This state has a bulk gap, no fractional charges or topological order in the bulk, but nevertheless quantized Hall transport and symmetry-protected edge excitations. Here we study a simple microscopic model for such a state in a system of two-component bosons in a strong orbital magnetic field. We show through exact-diagonalization calculations that the model supports the boson integer quantum Hall ground state in a range of parameters.