145,413 research outputs found
Elastic Instability Triggered Pattern Formation
Recent experiments have exploited elastic instabilities in membranes to
create complex patterns. However, the rational design of such structures poses
many challenges, as they are products of nonlinear elastic behavior. We pose a
simple model for determining the orientational order of such patterns using
only linear elasticity theory which correctly predicts the outcomes of several
experiments. Each element of the pattern is modeled by a "dislocation dipole"
located at a point on a lattice, which then interacts elastically with all
other dipoles in the system. We explicitly consider a membrane with a square
lattice of circular holes under uniform compression and examine the changes in
morphology as it is allowed to relax in a specified direction.Comment: 15 pages, 7 figures, the full catastroph
Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet
The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg
spins of large spin length is a highly frustrated model with an macroscopic
degeneracy of classical ground states. The zero-point energy of (harmonic
order) spin wave fluctuations distinguishes a subset of these states. I derive
an approximate but illuminating {\it effective Hamiltonian}, acting within the
subspace of Ising spin configurations representing the {\it collinear} ground
states. It consists of products of Ising spins around loops, i.e has the form
of a lattice gauge theory. The remaining ground state entropy is still
infinite but not extensive, being for system size . All these
ground states have unit cells bigger than those considered previously.Comment: 4pp, one figur
Lie Algebraic Similarity Transformed Hamiltonians for Lattice Model Systems
We present a class of Lie algebraic similarity transformations generated by
exponentials of two-body on-site hermitian operators whose Hausdorff series can
be summed exactly without truncation. The correlators are defined over the
entire lattice and include the Gutzwiller factor
, and two-site products of density
and spin
operators. The resulting non-hermitian many-body Hamiltonian can be solved in a
biorthogonal mean-field approach with polynomial computational cost. The
proposed similarity transformation generates locally weighted orbital
transformations of the reference determinant. Although the energy of the model
is unbound, projective equations in the spirit of coupled cluster theory lead
to well-defined solutions. The theory is tested on the 1D and 2D repulsive
Hubbard model where we find accurate results across all interaction strengths.Comment: The supplemental material is include
Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles
We discuss recent developments for exact reformulations of lattice field
theories in terms of worldlines and worldsheets. In particular we focus on a
strategy which is applicable also to non-abelian theories: traces and
matrix/vector products are written as explicit sums over color indices and a
dual variable is introduced for each individual term. These dual variables
correspond to fluxes in both, space-time and color for matter fields (Abelian
color fluxes), or to fluxes in color space around space-time plaquettes for
gauge fields (Abelian color cycles). Subsequently all original degrees of
freedom, i.e., matter fields and gauge links, can be integrated out.
Integrating over complex phases of matter fields gives rise to constraints that
enforce conservation of matter flux on all sites. Integrating out phases of
gauge fields enforces vanishing combined flux of matter- and gauge degrees of
freedom. The constraints give rise to a system of worldlines and worldsheets.
Integrating over the factors that are not phases (e.g., radial degrees of
freedom or contributions from the Haar measure) generates additional weight
factors that together with the constraints implement the full symmetry of the
conventional formulation, now in the language of worldlines and worldsheets. We
discuss the Abelian color flux and Abelian color cycle strategies for three
examples: the SU(2) principal chiral model with chemical potential coupled to
two of the Noether charges, SU(2) lattice gauge theory coupled to staggered
fermions, as well as full lattice QCD with staggered fermions. For the
principal chiral model we present some simulation results that illustrate
properties of the worldline dynamics at finite chemical potentials.Comment: Contribution to LATTICE 2017, 16 page
Dynamical mean-field theory for light fermion--heavy boson mixtures on optical lattices
We theoretically analyze Fermi-Bose mixtures consisting of light fermions and
heavy bosons that are loaded into optical lattices (ignoring the trapping
potential). To describe such mixtures, we consider the Fermi-Bose version of
the Falicov-Kimball model on a periodic lattice. This model can be exactly
mapped onto the spinless Fermi-Fermi Falicov-Kimball model at zero temperature
for all parameter space as long as the mixture is thermodynamically stable. We
employ dynamical mean-field theory to investigate the evolution of the
Fermi-Bose Falicov-Kimball model at higher temperatures. We calculate spectral
moment sum rules for the retarded Green's function and self-energy, and use
them to benchmark the accuracy of our numerical calculations, as well as to
reduce the computational cost by exactly including the tails of infinite
summations or products. We show how the occupancy of the bosons,
single-particle many-body density of states for the fermions, momentum
distribution, and the average kinetic energy evolve with temperature. We end by
briefly discussing how to experimentally realize the Fermi-Bose Falicov-Kimball
model in ultracold atomic systems.Comment: 10 pages with 4 figure
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