Quantum phases of strongly-interacting bosons on a two-leg Haldane ladder

We study the ground-state physics of a single-component Haldane model on a hexagonal two-leg ladder geometry with a particular focus on strongly interacting bosonic particles. We concentrate our analysis on the regime of less than one particle per unit-cell. As a main result, we observe several Meissner-like and vortex-fluid phases both for a superfluid as well as a Mott-insulating background. Furthermore, we show that for strongly interacting bosonic particles an unconventional vortex-lattice phase emerges, which is stable even in the regime of hardcore bosons. We discuss the mechanism for its stabilization for finite interactions by a means of an analytical approximation. We show how the different phases may be discerned by measuring the nearest- and next-nearest-neighbor chiral currents as well as their characteristic momentum distributions.Comment: 13 pages, 20 figure

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

Motivated by recent experiments, we study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. Using exact diagonalization and the density matrix renormalization group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. Typically, the relaxation to stationary values occurs over just a few tunneling times. The stationary values are identical to the so-called diagonal ensemble on the system sizes accessible to our numerical methods and we further observe that the micro-canonical ensemble describes the steady state of many observables reasonably well for small and intermediate interaction strength. The expectation values of observables in the canonical ensemble agree quantitatively with the time averages obtained from the quench at small interaction strengths, and qualitatively provide a good description of steady-state values even in parameter regimes where the micro-canonical ensemble is not applicable due to finite-size effects. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis. Moreover, we also observe that the diagonal and the canonical ensemble are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Finally, we discuss implications of our results for the interpretation of a recent sudden expansion experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction quench was realized.Comment: 19 pages, 22 figure

Carbon dioxide and fruit odor transduction in Drosophila olfactory neurons. What controls their dynamic properties?

We measured frequency response functions between odorants and action potentials in two types of neurons in Drosophila antennal basiconic sensilla. CO2 was used to stimulate ab1C neurons, and the fruit odor ethyl butyrate was used to stimulate ab3A neurons. We also measured frequency response functions for light-induced action potential responses from transgenic flies expressing H134R-channelrhodopsin-2 (ChR2) in the ab1C and ab3A neurons. Frequency response functions for all stimulation methods were well-fitted by a band-pass filter function with two time constants that determined the lower and upper frequency limits of the response. Low frequency time constants were the same in each type of neuron, independent of stimulus method, but varied between neuron types. High frequency time constants were significantly slower with ethyl butyrate stimulation than light or CO2 stimulation. In spite of these quantitative differences, there were strong similarities in the form and frequency ranges of all responses. Since light-activated ChR2 depolarizes neurons directly, rather than through a chemoreceptor mechanism, these data suggest that low frequency dynamic properties of Drosophila olfactory sensilla are dominated by neuron-specific ionic processes during action potential production. In contrast, high frequency dynamics are limited by processes associated with earlier steps in odor transduction, and CO2 is detected more rapidly than fruit odor

Low-lying zeros in families of elliptic curve L-functions over function fields

We investigate the low-lying zeros in families of L-functions attached to quadratic and cubic twists of elliptic curves defined over Fq(T). In particular, we present precise expressions for the expected values of traces of high powers of the Frobenius class in these families with a focus on the lower order behavior. As an application we obtain results on one-level densities and we verify that these elliptic curve families have orthogonal symmetry type. In the quadratic twist families our results refine previous work of Comeau-Lapointe. Moreover, in this case we find a lower order term in the one-level density reminiscent of the deviation term found by Rudnick in the hyperelliptic ensemble. On the other hand, our investigation is the first to treat these questions in families of cubic twists of elliptic curves and in this case it turns out to be more complicated to isolate lower order terms due to a larger degree of cancellation among lower order contributions

Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder

We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, inter-leg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.Comment: 4 pages + Supplementary Materia

Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: Swimming against the tide

The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While non-interacting as well as strongly interacting particles, stirred by the magnetic field, circulate along the system's boundary in the counterclockwise direction in the ground state, interactions stabilize vortex lattices. These states break translational symmetry, which can lead to a reversal of the circulation direction. Our predictions could readily be accessed in quantum gas experiments with existing setups or in arrays of Josephson junctions.Comment: 5 pages + 5 pages of supplementary materia