Few-body clusters in a multiband Hubbard model: Tetramers, pentamers, and beyond

We start with a variational approach and derive a set of coupled integral equations for the exact solutions of the bound states of $N$ identical spin-$\uparrow$ fermions and a single spin-$\downarrow$ fermion in a generic multiband Hubbard Hamiltonian with onsite attractive interactions. As an illustration we apply the integral equations to the so-called sawtooth lattice up to $N = 3$, i.e., to the $(3+1)$-body problem, due in part to its flat one-body band and one-dimensional simplicity, and most importantly to our benchmarking capacity with the DMRG simulations and exact diagonalization. Our numerical results reveal not only the presence of tetramer states in this two-band model but also their quasi-flat dispersion when formed in a flat one-body band. For $N = \{4, 5, \cdots, 10 \}$ our DMRG simulations and exact diagonalization suggest the presence of larger and larger multimers with lower and lower binding energies, conceivably without an upper bound on $N$ and with a quasi-flat dispersion when formed in a flat one-body band. These peculiar $(N+1)$-body clusters are in sharp contrast with the exact results on the single-band linear-chain model where none of the $N \ge 2$ multimers appear.Comment: 6+4 pages with 2+2 figure

Neural-network quantum states for a two-leg Bose-Hubbard ladder under magnetic flux

Quantum gas systems are ideal analog quantum simulation platforms for tackling some of the most challenging problems in strongly correlated quantum matter. However, they also expose the urgent need for new theoretical frameworks. Simple models in one dimension, well studied with conventional methods, have received considerable recent attention as test cases for new approaches. Ladder models provide the logical next step, where established numerical methods are still reliable, but complications of higher dimensional effects like gauge fields can be introduced. In this paper, we investigate the application of the recently developed neural-network quantum states in the two-leg Bose-Hubbard ladder under strong synthetic magnetic fields. Based on the restricted Boltzmann machine and feedforward neural network, we show that variational neural networks can reliably predict the superfluid-Mott insulator phase diagram in the strong coupling limit comparable with the accuracy of the density-matrix renormalization group. In the weak coupling limit, neural networks also diagnose other many-body phenomena such as the vortex, chiral, and biased-ladder phases. Our work demonstrates that the two-leg Bose-Hubbard model with magnetic flux is an ideal test ground for future developments of neural-network quantum states.Comment: 9 pages, 5 figure

Vortex lattices in dipolar two-component Bose-Einstein condensates

We consider a rapidly rotating two-component Bose-Einstein condensate with short-range s-wave interactions as well as dipolar coupling. We calculate the phase diagram of vortex lattice structures as a function of the intercomponent s-wave interaction and the strength of the dipolar interaction. We find that the long-range interactions cause new vortex lattice structures to be stable and lead to a richer phase diagram. Our results reduce to the previously found lattice structures for short-range interactions and single-component dipolar gases in the corresponding limits.Comment: 5 pages, 3 figure

Vortex Lattices in Strongly Confined Quantum Droplets

Bose mixture quantum droplets display a fascinating stability that relies on quantum fluctuations to prevent collapse driven by mean-field effects. Most droplet research focuses on untrapped or weakly trapped scenarios, where the droplets exhibit a liquid-like flat density profile. When weakly trapped droplets rotate, they usually respond through center-of-mass motion or splitting instability. Here, we study rapidly rotating droplets in the strong external confinement limit where the external potential prevents splitting and the center-of-mass excitation. We find that quantum droplets form a triangular vortex lattice as in single-component repulsive Bose-Einstein condensates (BEC), but the overall density follows the analytical Thomas-Fermi profile obtained from a cubic equation. We observe three significant differences between rapidly rotating droplets and repulsive BECs. First, the vortex core size changes markedly at finite density, visible in numerically obtained density profiles. We analytically estimate the vortex core sizes from the droplets' coherence length and find good agreement with the numerical results. Second, the change in the density profile gives a slight but observable distortion to the lattice, which agrees with the distortion expected due to nonuniform superfluid density. Lastly, unlike a repulsive BEC, which expands substantially as the rotation frequency approaches the trapping frequency, rapidly rotating droplets show only a fractional change in their size. We argue that this last point can be used to create clouds with lower filling factors, which may facilitate reaching the elusive strongly correlated regime

Ground-state properties, vortices, and collective excitations in a two-dimensional Bose-Einstein condensate with gravitylike interatomic attraction

We study the ground-state properties of a Bose-Einstein condensate with short-range repulsion and gravitylike 1/r interatomic attraction in two-dimensions (2D). Using the variational approach we obtain the ground-state energy and analyze the stability of the condensate for a range of interaction strengths in 2D. We also determine the collective excitations at zero temperature using the time-dependent variational method. We analyze the properties of the Thomas-Fermi-gravity and gravity regimes, and we examine the vortex states, finding the coherence length and monopole mode frequency for these regimes. Our results are compared and contrasted with those in 3D condensates. © 2008 The American Physical Society

Ground-State properties and collective excitations in a 2D Bose-Einstein condensate with gravity-like interatomic attraction

We study the ground-state properties of a Bose-Einstein condensate (BEC) with the short-range repulsion and gravitylike 1/r interatomic attraction in two-dimensions (2D). Using the variational approach, we obtain the ground-state energy and show that the condensate is stable for all interaction strenghts in 2D. We also determine the collective excitations at zero temperature using the time-dependent variational method. We analyze the properties of the Thomas-Fermi-gravity (TF-G) and gravity (G) regimes. © Springer Science+Business Media, LLC 2007

A visual pathway for skylight polarization processing in Drosophila

Many insects use patterns of polarized light in the sky to orient and navigate. Here, we functionally characterize neural circuitry in the fruit fly, Drosophila melanogaster, that conveys polarized light signals from the eye to the central complex, a brain region essential for the fly’s sense of direction. Neurons tuned to the angle of polarization of ultraviolet light are found throughout the anterior visual pathway, connecting the optic lobes with the central complex via the anterior optic tubercle and bulb, in a homologous organization to the ‘sky compass’ pathways described in other insects. We detail how a consistent, map-like organization of neural tunings in the peripheral visual system is transformed into a reduced representation suited to flexible processing in the central brain. This study identifies computational motifs of the transformation, enabling mechanistic comparisons of multisensory integration and central processing for navigation in the brains of insects

A Statistical Framework for the Analysis of ChIP-Seq Data

Chromatin immunoprecipitation followed by sequencing (ChIP-Seq) has revolutionalized experiments for genome-wide profiling of DNA-binding proteins, histone modifications, and nucleosome occupancy. As the cost of sequencing is decreasing, many researchers are switching from microarray-based technologies (ChIP-chip) to ChIP-Seq for genome-wide study of transcriptional regulation. Despite its increasing and well-deserved popularity, there is little work that investigates and accounts for sources of biases in the ChIP-Seq technology. These biases typically arise from both the standard pre-processing protocol and the underlying DNA sequence of the generated data