483 research outputs found
A flow equation approach to periodically driven quantum systems
We present a theoretical method to generate a highly accurate {\em
time-independent} Hamiltonian governing the finite-time behavior of a
time-periodic system. The method exploits infinitesimal unitary transformation
steps, from which renormalization group-like flow equations are derived to
produce the effective Hamiltonian. Our tractable method has a range of validity
reaching into frequency regimes that are usually inaccessible via high
frequency expansions in the parameter , where is the
upper limit for the strength of local interactions. We demonstrate our approach
on both interacting and non-interacting many-body Hamiltonians where it offers
an improvement over the more well-known Magnus expansion and other high
frequency expansions. For the interacting models, we compare our approximate
results to those found via exact diagonalization. While the approximation
generally performs better globally than other high frequency approximations,
the improvement is especially pronounced in the regime of lower frequencies and
strong external driving. This regime is of special interest because of its
proximity to the resonant regime where the effect of a periodic drive is the
most dramatic. Our results open a new route towards identifying novel
non-equilibrium regimes and behaviors in driven quantum many-particle systems.Comment: 25 pages, 14 figure
Floquet topological transitions in extended Kane-Mele models with disorder
In this work we use Floquet theory to theoretically study the influence of
circularly polarized light on disordered two-dimensional models exhibiting
topological transitions. We find circularly polarized light can induce a
topological transition in extended Kane-Mele models that include additional
hopping terms and on-site disorder. The topological transitions are understood
from the Floquet-Bloch band structure of the clean system at high symmetry
points in the first Brillouin zone. The light modifies the equilibrium band
structure of the clean system in such a way that the smallest gap in the
Brillouin zone can be shifted from the points to the points, the
point, or even other lower symmetry points. The movement of the
minimal gap point through the Brillouin zone as a function of laser parameters
is explained in the high frequency regime through the Magnus expansion. In the
disordered model, we compute the Bott index to reveal topological phases and
transitions. The disorder can induce transitions from topologically non-trivial
states to trivial states or vice versa, both examples of Floquet topological
Anderson transitions. As a result of the movement of the minimal gap point
through the Brillouin zone as a function of laser parameters, the nature of the
topological phases and transitions is laser-parameter dependent--a contrasting
behavior to the Kane-Mele model.Comment: 10 pages, 7 figure
Ordering in a frustrated pyrochlore antiferromagnet proximate to a spin liquid
We perform a general study of spin ordering on the pyrochlore lattice with a
3:1 proportionality of two spin polarizations. Equivalently, this describes
valence bond solid conformations of a quantum dimer model on the diamond
lattice. We determine the set of likely low temperature ordered phases, on the
assumption that the ordering is weak, i.e the system is close to a ``U(1)''
quantum spin liquid in which the 3:1 proportionality is maintained but the
spins are strongly fluctuating. The nature of the 9 ordered states we find is
determined by a ``projective symmetry'' analysis. All the phases exhibit
translational and rotational symmetry breaking, with an enlarged unit cell
containing 4 to 64 primitive cells of the underlying pyrochlore. The simplest
of the 9 phases is the same ``R'' state found earlier in a theoretical study of
the ordering on the magnetization plateau in the materials \cdaf and
\hgaf. We suggest that the spin/dimer model proposed therein undergoes a direct
transition from the spin liquid to the R state, and describe a field theory for
the universal properties of this critical point, at zero and non-zero
temperatures
Effective Hamiltonians for some highly frustrated magnets
In prior work, the authors developed a method of degenerate perturbation
theory about the Ising limit to derive an effective Hamiltonian describing
quantum fluctuations in a half-polarized magnetization plateau on the
pyrochlore lattice. Here, we extend this formulation to an arbitrary lattice of
corner sharing simplexes of sites, at a fraction of the
saturation magnetization, with . We present explicit effective
Hamiltonians for the examples of the checkerboard, kagome, and pyrochlore
lattices. The consequent ground states in these cases for are also
discussed.Comment: 10 pages, 2 figures,. Conference proceedings for Highly Frustrated
Magnetism 200
Analogue of Hamilton-Jacobi theory for the time-evolution operator
In this paper we develop an analogue of Hamilton-Jacobi theory for the
time-evolution operator of a quantum many-particle system. The theory offers a
useful approach to develop approximations to the time-evolution operator, and
also provides a unified framework and starting point for many well-known
approximations to the time-evolution operator. In the important special case of
periodically driven systems at stroboscopic times, we find relatively simple
equations for the coupling constants of the Floquet Hamiltonian, where a
straightforward truncation of the couplings leads to a powerful class of
approximations. Using our theory, we construct a flow chart that illustrates
the connection between various common approximations, which also highlights
some missing connections and associated approximation schemes. These missing
connections turn out to imply an analytically accessible approximation that is
the "inverse" of a rotating frame approximation and thus has a range of
validity complementary to it. We numerically test the various methods on the
one-dimensional Ising model to confirm the ranges of validity that one would
expect from the approximations used. The theory provides a map of the relations
between the growing number of approximations for the time-evolution operator.
We describe these relations in a table showing the limitations and advantages
of many common approximations, as well as the new approximations introduced in
this paper.Comment: 17 pages, 5 figures, 1 tabl
Nanoscale -Nuclear Magnetic Resonance Depth Imaging of Topological Insulators
Considerable evidence suggests that variations in the properties of
topological insulators (TIs) at the nanoscale and at interfaces can strongly
affect the physics of topological materials. Therefore, a detailed
understanding of surface states and interface coupling is crucial to the search
for and applications of new topological phases of matter. Currently, no methods
can provide depth profiling near surfaces or at interfaces of topologically
inequivalent materials. Such a method could advance the study of interactions.
Herein we present a non-invasive depth-profiling technique based on -NMR
spectroscopy of radioactive Li ions that can provide "one-dimensional
imaging" in films of fixed thickness and generates nanoscale views of the
electronic wavefunctions and magnetic order at topological surfaces and
interfaces. By mapping the Li nuclear resonance near the surface and 10 nm
deep into the bulk of pure and Cr-doped bismuth antimony telluride films, we
provide signatures related to the TI properties and their topological
non-trivial characteristics that affect the electron-nuclear hyperfine field,
the metallic shift and magnetic order. These nanoscale variations in
-NMR parameters reflect the unconventional properties of the topological
materials under study, and understanding the role of heterogeneities is
expected to lead to the discovery of novel phenomena involving quantum
materials.Comment: 46 pages, 12 figures in Proc. Natl. Aca. Sci. USA (2015) Published
online - early editio
Reinforcement learning in populations of spiking neurons
Population coding is widely regarded as a key mechanism for achieving reliable behavioral responses in the face of neuronal variability. But in standard reinforcement learning a flip-side becomes apparent. Learning slows down with increasing population size since the global reinforcement becomes less and less related to the performance of any single neuron. We show that, in contrast, learning speeds up with increasing population size if feedback about the populationresponse modulates synaptic plasticity in addition to global reinforcement. The two feedback signals (reinforcement and population-response signal) can be encoded by ambient neurotransmitter concentrations which vary slowly, yielding a fully online plasticity rule where the learning of a stimulus is interleaved with the processing of the subsequent one. The assumption of a single additional feedback mechanism therefore reconciles biological plausibility with efficient learning
Many-body theory of the quantum mirage
In recent scanning tunneling microscopy experiments, confinement in an
elliptical corral has been used to project the Kondo effect from one focus to
the other one. I solve the Anderson model at arbitrary temperatures, for an
impurity hybridized with eigenstates of an elliptical corral, each of which has
a resonant level width delta. This width is crucial. If delta < 20 meV, the
Kondo peak disappears, while if delta > 80 meV, the mirage disappears. For
particular conditions, a stronger mirage with the impurity out of the foci is
predicted.Comment: 5 pages, 5 figures. Some clarifications of the method added, and a
reference included to show that the hybridization of the impurity with bulk
states can be neglecte
Singular responses of spin-incoherent Luttinger liquids
When a local potential changes abruptly in time, an electron gas shifts to a
new state which at long times is orthogonal to the one in the absence of the
local potential. This is known as Anderson's orthogonality catastrophe and it
is relevant for the so-called X-ray edge or Fermi edge singularity, and for
tunneling into an interacting one dimensional system of fermions. It often
happens that the finite frequency response of the photon absorption or the
tunneling density of states exhibits a singular behavior as a function of
frequency: where is a
threshold frequency and is an exponent characterizing the singular
response. In this paper singular responses of spin-incoherent Luttinger liquids
are reviewed. Such responses most often do not fall into the familiar form
above, but instead typically exhibit logarithmic corrections and display a much
higher universality in terms of the microscopic interactions in the theory.
Specific predictions are made, the current experimental situation is
summarized, and key outstanding theoretical issues related to spin-incoherent
Luttinger liquids are highlighted.Comment: 21 pages, 3 figures. Invited Topical Review Articl
Floquet Hofstadter Butterfly on the Kagome and Triangular Lattices
In this work we use Floquet theory to theoretically study the influence of
monochromatic circularly and linearly polarized light on the Hofstadter
butterfly---induced by a uniform perpendicular magnetic field--for both the
kagome and triangular lattices. In the absence of the laser light, the
butterfly has fractal structure with inversion symmetry about magnetic flux
, and reflection symmetry about . As the system is exposed
to an external laser, we find circularly polarized light deforms the butterfly
by breaking the mirror symmetry at flux . By contrast, linearly
polarized light deforms the original butterfly while preserving the mirror
symmetry at flux . We find the inversion symmetry is always preserved
for both linear and circular polarized light. For linearly polarized light, the
Hofstadter butterfly depends on the polarization direction. Further, we study
the effect of the laser on the Chern number of lowest band in the off-resonance
regime (laser frequency is larger than the bandwidth). For circularly polarized
light, we find that low laser intensity will not change the Chern number, but
beyond a critical intensity the Chern number will change. For linearly
polarized light, the Chern number depends on the polarization direction. Our
work highlights the generic features expected for the periodically driven
Hofstadter problem on different lattices.Comment: 13 pages, 11 figure
- …