9,438 research outputs found
Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice
Ultracold atoms in optical lattices serve as a tool to model different
physical phenomena appearing originally in condensed matter.
To study magnetic phenomena one needs to engineer synthetic fields as atoms
are neutral.
Appropriately shaped optical potentials force atoms to mimic charged
particles moving in a given field. We present the realization of artificial
gauge fields for the observation of anomalous Hall effect. Two species of
attractively interacting ultracold fermions are considered to be trapped in a
shaken two dimensional triangular lattice. A combination of interaction induced
tunneling and shaking can result in an emergent Dice lattice. In such a lattice
the staggered synthetic magnetic flux appears and it can be controlled with
external parameters. The obtained synthetic fields are non-Abelian. Depending
on the tuning of the staggered flux we can obtain either anomalous Hall effect
or its quantized version. Our results are reminiscent of Anomalous Hall
conductivity in spin-orbit coupled ferromagnets.Comment: modified versio
Improved Smoothing Algorithms for Lattice Gauge Theory
The relative smoothing rates of various gauge field smoothing algorithms are
investigated on -improved \suthree Yang--Mills gauge field
configurations. In particular, an -improved version of APE
smearing is motivated by considerations of smeared link projection and cooling.
The extent to which the established benefits of improved cooling carry over to
improved smearing is critically examined. We consider representative gauge
field configurations generated with an -improved gauge field
action on \1 lattices at and \2 lattices at
having lattice spacings of 0.165(2) fm and 0.077(1) fm respectively. While the
merits of improved algorithms are clearly displayed for the coarse lattice
spacing, the fine lattice results put the various algorithms on a more equal
footing and allow a quantitative calibration of the smoothing rates for the
various algorithms. We find the relative rate of variation in the action may be
succinctly described in terms of simple calibration formulae which accurately
describe the relative smoothness of the gauge field configurations at a
microscopic level
Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow
Leaving a few exceptions aside, cellular automata (CA) and the intimately related coupled-map lattices (CML), commonly known as continuous cellular automata (CCA), as well as models that are based upon one of these paradigms, employ a regular tessellation of an Euclidean space in spite of the various drawbacks this kind of tessellation entails such as its inability to cover surfaces with an intricate geometry, or the anisotropy it causes in the simulation results. Recently, a CCA-based model describing steady-state heat flow has been proposed as an alternative to Laplace's equation that is, among other things, commonly used to describe this process, yet, also this model suffers from the aforementioned drawbacks since it is based on the classical CCA paradigm. To overcome these problems, we first conceive CCA on irregular tessellations of an Euclidean space after which we show how the presented approach allows a straightforward simulation of steady-state heat flow on surfaces with an intricate geometry, and, as such, constitutes an full-fledged alternative for the commonly used and easy-to-implement finite difference method, and the more intricate finite element method
Three dimensional resonating valence bond liquids and their excitations
We show that there are two types of RVB liquid phases present in
three-dimensional quantum dimer models, corresponding to the deconfining phases
of U(1) and Z_2 gauge theories in d=3+1. The former is found on the bipartite
cubic lattice and is the generalization of the critical point in the square
lattice quantum dimer model found originally by Rokhsar and Kivelson. The
latter exists on the non-bipartite face-centred cubic lattice and generalizes
the RVB phase found earlier by us on the triangular lattice. We discuss the
excitation spectrum and the nature of the ordering in both cases. Both phases
exhibit gapped spinons. In the U(1) case we find a collective, linearly
dispersing, transverse excitation, which is the photon of the low energy
Maxwell Lagrangian and we identify the ordering as quantum order in Wen's
sense. In the Z_2 case all collective excitations are gapped and, as in d=2,
the low energy description of this topologically ordered state is the purely
topological BF action. As a byproduct of this analysis, we unearth a further
gapless excitation, the pi0n, in the square lattice quantum dimer model at its
critical point.Comment: 9 pages, 2 figure
Short-ranged RVB physics, quantum dimer models and Ising gauge theories
Quantum dimer models are believed to capture the essential physics of
antiferromagnetic phases dominated by short-ranged valence bond configurations.
We show that these models arise as particular limits of Ising (Z_2) gauge
theories, but that in these limits the system develops a larger local U(1)
invariance that has different consequences on different lattices. Conversely,
we note that the standard Z_2 gauge theory is a generalised quantum dimer
model, in which the particular relaxation of the hardcore constraint for the
dimers breaks the U(1) down to Z_2. These mappings indicate that at least one
realization of the Senthil-Fisher proposal for fractionalization is exactly the
short ranged resonating valence bond (RVB) scenario of Anderson and of
Kivelson, Rokhsar and Sethna. They also suggest that other realizations will
require the identification of a local low energy, Ising link variable {\it and}
a natural constraint. We also discuss the notion of topological order in Z_2
gauge theories and its connection to earlier ideas in RVB theory. We note that
this notion is not central to the experiment proposed by Senthil and Fisher to
detect vortices in the conjectured Z_2 gauge field.Comment: 17 pages, 4 postscript figures automatically include
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