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Register a new userDevils staircases without particle-hole symmetry
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We present and analyze spin models with long-range interactions whose ground state features a so-called devils staircase and where plateaus of the staircase are accessed by varying two-body interactions. This is in contrast to the canonical devils staircase, for example occurring in the one-dimensional Ising model with long-range interactions, where typically a single-body chemical potential is varied to scan through the plateaus. These systems, moreover, typically feature a particle-hole symmetry which trivially connects the hole part of the staircase (filling fraction $fgeq1/2$) to its particle part ($fleq1/2$). Such symmetry is absent in our models and hence the particle sector and the hole sector can be separately controlled, resulting in exotic hybrid staircases.
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The devils staircase is a fractal structure that characterizes the ground state of one-dimensional classical lattice gases with long-range repulsive convex interactions. Its plateaus mark regions of stability for specific filling fractions which are controlled by a chemical potential. Typically such staircase has an explicit particle-hole symmetry, i.e., the staircase at more than half-filling can be trivially extracted from the one at less than half filling by exchanging the roles of holes and particles. Here we introduce a quantum spin chain with competing short-range attractive and long-range repulsive interactions, i.e. a non-convex potential. In the classical limit the ground state features generalized Wigner crystals that --- depending on the filling fraction --- are either composed of dimer particles or dimer holes which results in an emergent complete devils staircase without explicit particle-hole symmetry of the underlying microscopic model. In our system the particle-hole symmetry is lifted due to the fact that the staircase is controlled through a two-body interaction rather than a one-body chemical potential. The introduction of quantum fluctuations through a transverse field melts the staircase and ultimately makes the system enter a paramagnetic phase. For intermediate transverse field strengths, however, we identify a region, where the density-density correlations suggest the emergence of quasi long-range order. We discuss how this physics can be explored with Rydberg-dressed atoms held in a lattice.
We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of dominant products to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamical polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a a matrix-free GMRES method to determine the (interacting) density response. The resulting code is about one order of magnitude faster than our previous full-matrix method. This acceleration makes the speed of our TDDFT code comparable with codes based on Casidas equation. The implementation of our method uses hybrid MPI and OpenMP parallelization in which load balancing and memory access are optimized. To validate our approach and to establish benchmarks, we compute spectra of large molecules on various types of parallel machines. The methods developed here are fairly general and we believe they will find useful applications in molecular physics/chemistry, even for problems that are beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.
Motivated by recent experiments, we study normal-phase rotating He-3 droplets within Density Functional Theory in a semi-classical approach. The sequence of rotating droplet shapes as a function of angular momentum are found to agree with those of rotating classical droplets, evolving from axisymmetric oblate to triaxial prolate to two-lobed shapes as the angular momentum of the droplet increases. Our results, which are obtained for droplets of nanoscopic size, are rescaled to the mesoscopic size characterizing ongoing experimental measurements, allowing for a direct comparison of shapes. The stability curve in the angular velocity-angular momentum plane shows small deviations from the classical rotating drop model predictions, whose magnitude increases with angular momentum. We attribute these deviations to effects not included in the simplified classical model description of a rotating fluid held together by surface tension, i.e. to surface diffuseness, curvature and finite compressibility, and to quantum effects associated with deformation of the He-3 Fermi surface. The influence of all these effects is expected to diminish as the droplet size increases, making the classical rotating droplet model a quite accurate representation of He-3 rotation.
We present an experimental study of the Dynamic Nuclear Polarization (DNP) of si{} nuclei in silicon crystals of natural abundance doped with As in the temperature range 0.1-1 K and in strong magnetic field of 4.6 T. This ensures very high degree of electron spin polarization, extremely slow nuclear relaxation and optimal conditions for realization of Overhauser and resolved solid effects. We found that the solid effect DNP leads to an appearance of a pattern of holes and peaks in the ESR line, separated by the super-hyperfine interaction between the donor electron and si{} nuclei closest to the donor. On the contrary, the Overhauser effect DNP mainly affects the remote si{} nuclei having the weakest interaction with the donor electron. This leads to an appearance of a very narrow ($approx$ 3 mG wide) hole in the ESR line. We studied relaxation of the holes after burning, which is caused by the nuclear spin diffusion. Analyzing the spin diffusion data with a simple one-dimensional spectral diffusion model leads to a value of the spectral diffusion coefficient $D=8(3)times 10^{-3}$ mG$^2$/s. Our data indicate that the spin diffusion is not completely prevented even in the frozen core near the donors. The emergence of the narrow hole after the Overhauser DNP may be explained by a partial softening of the frozen core caused by Rabi oscillations of the electron spin.
A method to calculate the bound states of three-atoms without resorting to an explicit partial wave decomposition is presented. The differential form of the Faddeev equations in the total angular momentum representation is used for this purpose. The method utilizes Cartesian coordinates combined with the tensor-trick preconditioning for large linear systems and Arnoldis algorithm for eigenanalysis. As an example, we consider the He$_3$ system in which the interatomic force has a very strong repulsive core that makes the three-body calculations with standard methods tedious and cumbersome requiring the inclusion of a large number of partial waves. The results obtained compare favorably with other results in the field.
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