Bosonic Fractional Quantum Hall Research Articles

Excitonic topological order in imbalanced electron-hole bilayers.

Correlation and frustration play essential roles in physics, giving rise to novel quantum phases1-6. A typical frustrated system is correlated bosons on moat bands, which could host topological orders with long-range quantum entanglement4. However, the realization of moat-band physics is still challenging. Here, we explore moat-band phenomena in shallowly inverted InAs/GaSb quantum wells, where we observe an unconventional time-reversal-symmetry breaking excitonic ground state under imbalanced electron and hole densities. We find that a large bulk gap exists, encompassing a broad range of density imbalances at zero magnetic field (B), accompanied by edge channels that resemble helical transport. Under an increasing perpendicular B, the bulk gap persists, and an anomalous plateau of Hall signals appears, which demonstrates an evolution from helical-like to chiral-like edge transport with a Hall conductance approximately equal to e2/h at 35 tesla,where e is the elementarycharge and h is Planck's constant. Theoretically, we show that strong frustration from density imbalance leads to a moat band for excitons, resulting in a time-reversal-symmetry breaking excitonic topological order, which explains all our experimental observations. Our work opens up a new direction for research on topological and correlated bosonic systems in solid states beyond the framework of symmetry-protected topological phases, including but not limited to the bosonic fractional quantum Hall effect.

Double roton-minima in bosonic fractional quantum Hall states

We have studied the collective spin-conserving collective excitation spectra in rotating diluted ultra-cold Bose atoms. Double roton-minima have been observed in the fractional quantum Hall (FQH) states for the two filling fractions (ν) of the first series of Jain's composite fermion sequences. The obtained roton-minima for ν = 1/4 are at the wave-vectors 1.26 and 2.38 and the roton-minima for ν = 1/6 have been shifted to 1.08 and 2.06. Such shift of roton-minima is attributed due to strong correlation between the particles in bosonic FQH-system. Moreover, the number of roton minima observed depends upon number of attached fluxes as well as the ranges of interaction between the particles.

Chiral broken symmetry descendants of the kagome lattice chiral spin liquid

The breaking of chiral and time-reversal symmetries provides a pathway to exotic quantum phenomena and topological phases. Recent work has extensively explored the resulting emergence of chiral charge orders and chiral spin liquids (CSLs) on the kagome lattice. Such CSLs are closely tied to bosonic fractional quantum Hall states with anyonic quasiparticles; however, their connection to nearby ordered states has remained a mystery. Here, we use spin-wave theory, parton Gutzwiller wave functions, and exact diagonalization to show that two distinct magnetic orders with uniform scalar chirality---the XYZ umbrella state and the octahedral spin crystal--emerge as competing orders in close proximity to the CSL. In this letter, we highlight the intimate link between a topologically ordered liquid and broken symmetry states with nontrivial real-space topology.

Fractional quantum Hall effect in optical lattices

In this research, we study the bosonic fractional quantum Hall (FQH) states in a system of ultracold bosons in a two-dimensional optical lattice in the presence of a synthetic magnetic field, described by the bosonic Harper–Hofstadter Hamiltonian. We use the cluster Gutzwiller mean-field and exact diagonalization techniques in our work. We obtain incompressible states as ground states at various filling factors similar to those of the FQH states. We focus in particular on the ν = 1/2 FQH state, and it is characterized by the two-point correlation function and the many-body Chern number. We further investigate the effect of dipolar interaction on the ν = 1/2 FQH state. We find that the dipolar interaction stabilizes the FQH state against the competing superfluid state.

Bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices without flat bands

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 on the lattice shaking, and the fractional conductance is robust in the shaken lattice. This provides an easy way to initialize and prepare the fractional quantum Hall states in ultracold-atom platforms, and it paves the way to investigate and simulate strongly correlated quantum matters with degenerate quantum gas.

Quantum Hall states for Rydberg arrays with laser-assisted dipole-dipole interactions

Rydberg atoms with dipole-dipole interactions provide intriguing platforms to explore exotic quantum many-body physics. Here we propose a novel scheme with laser-assisted dipole-dipole interactions to realize synthetic magnetic field for Rydberg atoms in a two-dimensional array configuration, which gives rise to the exotic bosonic topological states. In the presence of an external effective Zeeman splitting gradient, the dipole-dipole interaction between neighboring Rydberg atoms along the gradient direction is suppressed, but can be assisted when Raman lights are applied to compensate the energy difference. With this scheme we generate a controllable uniform magnetic field for the complex spin-exchange coupling model, which can be mapped to hard core bosons coupling to an external synthetic magnetic field. The highly tunable flat Chern bands of the hard core bosons are then obtained and moreover, the bosonic fractional quantum Hall states can be achieved with experimental feasibility. This work opens an avenue for the realization of the highly-sought-after bosonic topological orders using Rydberg atoms.

Lowest Landau level theory of the bosonic Jain states

Quantum Hall systems offer the most familiar setting where strong inter-particle interactions combine with the topology of single particle states to yield novel phenomena. Despite our mature understanding of these systems, an open challenge has been to to develop a microscopic theory capturing both their universal and non-universal properties, when the Hamiltonian is restricted to the non-commutative space of the lowest Landau level. Here we develop such a theory for the Jain sequence of bosonic fractional quantum Hall states at fillings $\nu={p\over p+1}$. Building on a lowest Landau level description of a parent composite fermi liquid at $\nu = 1$, we describe how to dope the system to reach the Jain states. Upon doping, the composite fermions fill non-commutative generalizations of Landau levels, and the Jain states correspond to integer composite fermion filling. Using this approach, we obtain an approximate expression for the bosonic Jain sequence gaps with no reference to any long-wavelength approximation. Furthermore, we show that the universal properties, such as Hall conductivity, are encoded in an effective non-commutative Chern-Simons theory, which is obtained on integrating out the composite fermions. This theory has the same topological content as the familiar Abelian Chern-Simons theory on commutative space.

Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids

We present a microscopic study of quasiholes in bosonic fractional quantum Hall (FQH) liquids at filling factor $\nu=1/2$ in the lowest Landau level with anisotropic band mass tensors. We use the spatial density profile to characterize the shape of a quasihole and analyze its anisotropy. We then compare the quasihole's anisotropy with the intrinsic geometric metric of the system that is extracted from the maximal overlap between the numerically obtained quasihole ground state and a set of model wave functions of anisotropic quasiholes. For a static system, we find that the quasihole's anisotropy, similar to the intrinsic metric, grows with the anisotropy of the band mass tensor. When the quasihole develops well, we observe a correspondence between the anisotropy of the quasihole and the intrinsic metric of the underlying anisotropic FQH state. We also drive the system out of equilibrium by suddenly changing the band mass tensor. In this case, the shape of the quasihole evolves with time and shows similar dynamics with the intrinsic metric of the postquench state. The evolving frequency matches the energy of a spin-$2$ quadrupole degree of freedom in the system. Our results suggest that the density profile of a quasihole is a useful tool to estimate the intrinsic metric and capture the dynamics of an FQH system.

Disorder-driven phase transitions in bosonic fractional quantum Hall liquids

We investigate the disorder-driven phase transitions in bosonic fractional quantum Hall liquids at filling factors $f=1/2$ and $f=1$ in the lowest Landau level. We use the evolution of ground-state entanglement entropy, fidelity susceptibility, and Hall conductance with increasing disorder strength to identify the underlying phase transitions. The critical disorder strengths obtained from these different quantities are consistent with each other, validating the reliability of our numerical calculations based on exact diagonalization. At $f=1/2$, we observe a clear transition from the bosonic Laughlin state to a trivial insulating phase. At $f=1$, we identify a direct phase transition from the non-Abelian bosonic Moore-Read state to a trivial insulating phase, although some signs of a disorder-induced intermediate fractional quantum Hall phase were recently reported for the $f=5/2$ fermionic cousin.

Statistical Interactions and Boson-Anyon Duality in Fractional Quantum Hall Fluids.

We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For interacting electrons, the statistical transmutation from anyons to bosons allows us to explicitly derive the microscopic statistical interaction between the anyons, in the form of the effective two-body and few-body interactions. This also leads to a number of unexpected topological phases of the single component bosonic fractional quantum Hall effect that may be experimentally accessible. Numerical analysis of the energy spectrum and ground state entanglement properties are carried out for simple examples.

Floquet engineering flat bands for bosonic fractional quantum Hall with superconducting circuits

The quest to realize novel phases of matter with topological order is an important pursuit with implications for strongly correlated physics and quantum information. Utilizing ideas from state-of-the-art coherent control of artificial quantum systems such as superconducting circuits, we present a proposal to realize bosonic fractional quantum Hall physics on small lattices by creating nearly flat topological bands using staggered flux patterns. Fingerprints of fractionalization through charge pumping can be observed with nearly perfect quantization using as few as 24 lattice sites (two photons). We suggest an implementation using a finite lattice of superconducting qubits with cylindrical connectivity on both triangular and square lattices.

Phase transitions of bosonic fractional quantum Hall effect in topological flat bands

We study the phase transitions of bosonic $\ensuremath{\nu}=1/2$ 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 FQH liquid would turn into a superfluid state with a direct energy level crossing and a discontinuous leap of off-diagonal long-range order.

Bosonic fractional quantum Hall states in driven optical lattices

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 $\omega$, such that the stroboscopic dynamics supports the basic $\nu = 1/2$ Laughlin state. Moreover, we explore slow ramping of a driving term and show that the considered protocol allows for the preparation of the Laughlin state on experimentally realistic time scales.

Bosonic fractional quantum Hall states on a finite cylinder

We investigate the ground state properties of a bosonic Harper-Hofstadter model with local interactions on a finite cylindrical lattice with filling fraction $\nu=1/2$. 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 $\nu=1/2$ 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 large values of the magnetic flux density. Furthermore, we determine the dependence of the correlation functions and edge currents on the interaction strength. We find that depending on the magnetic flux density, the transition towards Laughlin-like behaviour can be either smooth or happens abruptly for some critical interaction strength.

Ring-shaped fractional quantum Hall liquids with hard-wall potentials

We study the physics of $\nu=1/2$ bosonic fractional quantum Hall droplets confined in a ring-shaped region delimited by two concentric cylindrically symmetric hard-wall potentials. Trial wave functions based on an extension of the Jack polynomial formalism including two different chiral edges are proposed and validated for a wide range of confinement potentials in terms of their excellent overlap with the eigenstates numerically found by exact diagonalization. In the presence of a single repulsive potential centered in the origin, a recursive structure in the many-body spectra and a massively degenerate ground state manifold are found. The addition of a second hard-wall potential confining the fractional quantum Hall droplet from the outside leads to a non-degenerate ground state containing a well defined number of quasiholes at the center and, for suitable potential parameters, to a clear organization of the excitations on the two edges. The utility of this ring-shaped configuration in view of theoretical and experimental studies of subtle aspects of fractional quantum Hall physics is outlined.

Topological phase transition in a two-species fermion system: Effects of a rotating trap potential or a synthetic gauge field

We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via $s$-wave Feshbach resonance, and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor $\nu_f = 2$. We show that the system undergoes a continuous quantum phase transition from a $\nu_f = 2$ fermionic integer quantum Hall state formed by atoms, to a $\nu_b = 1/2$ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field theoretical predictions, and the case of $p$-wave pairing.

Realizing and adiabatically preparing bosonic integer and fractional quantum Hall states in optical lattices

We study the ground states of 2D lattice bosons in an artificial gauge field. Using state of the art DMRG simulations we obtain the zero temperature phase diagram for hardcore bosons at densities $n_b$ with flux $n_\phi$ per unit cell, which determines a filling $\nu=n_b/n_\phi$. We find several robust quantum Hall phases, including (i) a bosonic integer quantum Hall phase (BIQH) at $\nu=2$, that realizes an interacting symmetry protected topological phase in 2D (ii) bosonic fractional quantum Hall phases including robust states at $\nu=2/3$ and a Laughlin state at $\nu=1/2$. The observed states correspond to the bosonic Jain sequence ($\nu=p/(p+1)$) pointing towards an underlying composite fermion picture. In addition to identifying Hamiltonians whose ground states realize these phases, we discuss their preparation beginning from independent chains, and ramping up interchain couplings. Using time dependent DMRG simulations, these are shown to reliably produce states close to the ground state for experimentally relevant system sizes. Besides the wave-function overlap, we utilize a simple physical signature of these phases, the non-monotonic behavior of a two-point correlation, a direct consequence of edge states in a finite system, to numerically assess the effectiveness of the preparation scheme. Our proposal only utilizes existing experimental capabilities.

Creating a bosonic fractional quantum Hall state by pairing fermions

We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case where each spin population is prepared in a quantum Hall state with unity filling, we follow the evolution of the system as the interaction strength is increased. Above a critical value and for sufficiently low flux density, we observe the emergence of a twofold quasidegeneracy accompanied by the opening of an energy gap to the third level. Analysis of the entanglement spectra shows that the gapped ground state is the bosonic $1/2$ Laughlin state. Our work therefore provides compelling evidence of a topological phase transition from the fermionic quantum Hall state at unity filling to the bosonic Laughlin state at a critical attraction strength.

Hard-wall confinement of a fractional quantum Hall liquid

We make use of numerical exact diagonalization calculations to explore the physics of $\nu = 1/2$ bosonic fractional quantum Hall (FQH) droplets in the presence of experimentally realistic cylindrically symmetric hard-wall potentials. This kind of confinement is found to produce very different many-body spectra compared to a harmonic trap or the so-called extremely steep limit. For a relatively weak confinement, the degeneracies are lifted and the low-lying excited states organize themselves in energy branches that can be explained in terms of their Jack polynomial representation. For a strong confinement, a strong spatial deformation of the droplet is found, with an unexpected depletion of its central density.

Global phase diagram and quantum spin liquids in a spin-12triangular antiferromagnet

We study the spin-$1/2$ Heisenberg model on the triangular lattice with the nearest-neighbor $J_1 > 0$, the next-nearest-neighobr $J_2 > 0$ Heisenberg interactions, and the additional scalar chiral interaction $J_{\chi}(\vec{S}_i \times \vec{S}_j) \cdot \vec{S}_k$ for the three spins in all the triangles using large-scale density matrix renormalization group calculation on cylinder geometry. With increasing $J_2$ ($J_2/J_1 \leq 0.3$) and $J_{\chi}$ ($J_{\chi}/J_1 \leq 1.0$) interactions, we establish a quantum phase diagram with the magnetically ordered $120^{\circ}$ phase, stripe phase, and non-coplanar tetrahedral phase. In between these magnetic order phases, we find a chiral spin liquid (CSL) phase, which is identified as a $\nu = 1/2$ bosonic fractional quantum Hall state with possible spontaneous rotational symmetry breaking. By switching on the chiral interaction, we find that the previously identified spin liquid in the $J_1 - J_2$ triangular model ($0.08 \lesssim J_2/J_1 \lesssim 0.15$) shows a phase transition to the CSL phase at very small $J_{\chi}$. We also compute spin triplet gap in both spin liquid phases, and our finite-size results suggest large gap in the odd topological sector but small or vanishing gap in the even sector. We discuss the implications of our results to the nature of the spin liquid phases.