We employ the exact diagonalization method to analyze the possibility of generating strongly correlated states in two-dimensional clouds of ultracold bosonic atoms which are subjected to a geometric gauge field created by coupling two internal atomic states to a laser beam. Tuning the gauge field strength, the system undergoes stepwise transitions between different ground states, which we describe by analytical trial wave functions, amongst them the Pfaffian, the Laughlin, and a Laughlin quasiparticle many-body state. The adiabatic following of the center of mass movement by the lowest energy dressed internal state, is lost by the mixing of the second internal state. This mixture can be controlled by the intensity of the laser field. The non-adiabaticity is inherent to the considered setup, and is shown to play the role of circular asymmetry. We study its influence on the properties of the ground state of the system. Its main effect is to reduce the overlap of the numerical solutions with the analytical trial expressions by occupying states with higher angular momentum. Thus, we propose generalized wave functions arising from the Laughlin and Pfaffian wave function by including components, where extra Jastrow factors appear, while preserving important features of these states. We analyze quasihole excitations over the Laughlin and generalized Laughlin states, and show that they possess effective fractional charge and obey anyonic statistics. Finally, we study the energy gap over the Laughlin state as the number of particles is increased keeping the chemical potential fixed. The gap is found to decrease as the number of particles is increased, indicating that the observability of the Laughlin state is restricted to a small number of particles.
We study the phase transitions of bosonic $ν=1/2$ fractional quantum Hall (FQH) effect in different topological lattice models under the interplay of onsite periodic potential and Hubbard repulsion. Through exact diagonalization and density matrix renormalization group methods, we demonstrate that the many-body ground state undergoes a continuous phase transition between bosonic FQH liquid and a trivial (Mott) insulator induced by the periodic potential, characterized by the smooth crossover of energy and entanglement entropy. When the Hubbard repulsion decreases, we claim that this bosonic FQ…
We propose a scheme to realize bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices. This scheme does not require a very flat band, and the necessary long-range interaction relies on s-wave scattering, which is common in many ultracold-atom experiments. By filling the lattice at 1/4 with identical bosons under Feshbach resonance, two degenerate many-body ground states share one Chern number of 1 and correspond exactly to the fractional quantum Hall conductance of 1/2. Meanwhile, we prove that the fractional quantum Hall state can be prepared by adiabatically turning…
We report a new many body phenomena called " Nearly order from quantum disorder phenomena" (NOFQD). We demonstrate the NOFQD in the experimentally realized weakly interacting Quantum Anomalous Hall system of spinor bosons in an optical lattice. We establish intrinsic connections between the phenomenological GL theory and the microscopic calculations on the effective potential. Connections with the bilayer quantum Hall system with a total filling factor $ ν_T=1 $ are made. Some insightful analogy with $ NAdS_2/NCFT_1 $ ( where $ N $ also means nearly ) correspondence in the context of Sachdev-Y…
Bosonic Fractional Quantum Hall States in Rotating Optical Lattices: Projective Symmetry Group Analysis
研究二维旋转正方形光晶格中玻色子的不可压缩基态。在由于晶格转动而产生的有效均匀磁场中，该系统可用玻色-哈伯德模型描述。为了研究该系统的基态，我们将其映射到一个阻挫自旋模型，然后用Schwinger玻色子平均场论和投影对称群分析。使用对称性分析，我们确定玻色子分数量子霍尔态，预测玻色子原子在旋转光晶格，与可能的稳定的带隙自旋液体状态内的Schwinger玻色子形式主义。特别地，我们发现先前发现的分数量子霍尔态是由晶格势诱导的，并且在连续谱中没有对应的量子霍尔态[G。Möller，and N. R. Cooper，Phys. Rev. Lett. \textbf{103}，105303（2009）]，对应于受抑自旋模型的“$π$通量”自旋液态。
We study an interacting two-component hard-core bosons on square lattice for which, in the presence of staggered magnetic flux, the ground state is a bosonic integer quantum Hall (BIQH) state. Using a coupled-wire bosonization approach, we analytically show this model exhibits a BIQH state at total charge half filling associated with a symmetry-protected topological phase under $U(1)$ charge conservation. These theoretical expectations are verified, using the infinite density matrix renormalization group method, by providing numerical evidences for: (i) a quantized Hall conductance $σ_{xy}=\pm…
The anomalous Hall effect has had a profound influence on the understanding of many electronic topological materials but is much less studied in their bosonic counterparts. We predict that an intrinsic anomalous Hall effect exists in a recently realized bosonic chiral superfluid, a $p$-band Bose-Einstein condensate in a 2D hexagonal boron nitride optical lattice [X. Wang et al., https://www.nature.com/articles/s41586-021-03702-0 Nature (London) 596, 227 (2021)]. We evaluate the frequency-dependent Hall conductivity within a multi-orbital Bose-Hubbard model that accurately captures the real exp…
We investigate the ground state properties of a bosonic Harper-Hofstadter model with local interactions on a finite cylindrical lattice with filling fraction $ν=1/2$. We find that our system supports topologically ordered states by calculating the topological entanglement entropy, and its value is in good agreement with the theoretical value for the $ν=1/2$ Laughlin state. By exploring the behaviour of the density profiles, edge currents and single-particle correlation functions, we find that the ground state on the cylinder shows all signatures of a fractional quantum Hall state even for larg…
We study $N$-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU$(N)$-invariant interactions based on density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU$(N)$ fractional quantum Hall states can emerge at fractional filling factors $ν=N/(N+1)$ for bosons ($ν=N/(2N+1)$ for fermions) in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characte…
Strong synthetic magnetic fields have been successfully implemented in periodically driven optical lattices. However, the interplay of the driving and interactions introduces detrimental heating, and for this reason it is still challenging to reach a fractional quantum Hall state in cold-atom setup. By performing a numerical study, we investigate stability of a bosonic Laughlin state in a small atomic sample exposed to driving. We identify an optimal regime of microscopic parameters, in particular interaction strength $U$ and the driving frequency $ω$, such that the stroboscopic dynamics suppo…
Univ Lyon, Ens de Lyon, CNRS, Laboratoire de Physique（里昂大学、巴黎高等师范学校里昂分校、法国国家科学研究中心、物理实验室）；Physics Department “E. R. Caianiello” and CNR-SPIN, Universitá degli Studi di Salerno, INFN, Gruppo Collegato di Salerno（萨莱诺大学“E.R.卡亚涅洛”物理系和CNR-SPIN研究所、意大利国家核物理研究所萨莱诺协作组）；DQMP, University of Geneva（日内瓦大学量子物质与凝聚态物理系）
The recent progress in engineering topological band structures in optical-lattice systems makes it promising to study fractional Chern insulator states in these systems. Here we consider a realistic finite system of a few repulsively interacting bosons on a square lattice with magnetic flux and sharp edges, as it can be realized in quantum-gas microscopes. We investigate under which conditions a fractional Chern insulator state corresponding to the Laughlin-like state at filling $ν=1/2$ can be stabilized and its fractional excitations probed. Using numerical simulations, we find an incompressi…
We develop a low-energy effective field theory of a two-dimensional bosonic superfluid on the lowest Landau level at zero temperature and identify a Berry term that governs the dynamics of coarse-grained superfluid degrees of freedom. For an infinite vortex crystal we compute how the Berry term affects the low-energy spectrum of soft collective Tkachenko oscillations and non-dissipative Hall responses of the particle number current and stress tensor. This term gives rise to a quadratic in momentum term in the Hall conductivity, but does not generate a non-dissipative Hall viscosity.
