440 research outputs found
Fast preparation of critical ground states using superluminal fronts
We propose a spatio-temporal quench protocol that allows for the fast
preparation of ground states of gapless models with Lorentz invariance.
Assuming the system initially resides in the ground state of a corresponding
massive model, we show that a superluminally-moving `front' that
quenches the mass, leaves behind it (in space) a state
to the ground state of the gapless model.
Importantly, our protocol takes time to produce
the ground state of a system of size ( spatial dimensions), while
a fully adiabatic protocol requires time
to produce a state with exponential accuracy in . The physics of the
dynamical problem can be understood in terms of relativistic rarefaction of
excitations generated by the mass front. We provide proof-of-concept by solving
the proposed quench exactly for a system of free bosons in arbitrary
dimensions, and for free fermions in . We discuss the role of
interactions and UV effects on the free-theory idealization, before numerically
illustrating the usefulness of the approach via simulations on the quantum
Heisenberg spin-chain.Comment: 4.25 + 10 pages, 3 + 2 figure
The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid
The Pfaffian phase of electrons in the proximity of a half-filled Landau
level is understood to be a p+ip superconductor of composite fermions. We
consider the properties of this paired quantum Hall phase when the pairing
scale is small, i.e. in the weak-coupling, BCS, limit, where the coherence
length is much larger than the charge screening length. We find that, as in a
Type I superconductor, the vortices attract so that, upon varying the magnetic
field from its magic value at \nu=5/2, the system exhibits Coulomb frustrated
phase separation. We propose that the weakly and strongly coupled Pfaffian
states exemplify a general dichotomy between Type I and Type II quantum Hall
fluids.Comment: 4 pages, 1 figur
The Kibble-Zurek Problem: Universality and the Scaling Limit
Near a critical point, the equilibrium relaxation time of a system diverges
and any change of control/thermodynamic parameters leads to non-equilibrium
behavior. The Kibble-Zurek problem is to determine the dynamical evolution of
the system parametrically close to its critical point when the change is
parametrically slow. The non-equilibrium behavior in this limit is controlled
entirely by the critical point and the details of the trajectory of the system
in parameter space (the protocol) close to the critical point. Together, they
define a universality class consisting of critical exponents-discussed in the
seminal work by Kibble and Zurek-and scaling functions for physical quantities,
which have not been discussed hitherto. In this article, we give an extended
and pedagogical discussion of the universal content in the Kibble-Zurek
problem. We formally define a scaling limit for physical quantities near
classical and quantum transitions for different sets of protocols. We report
computations of a few scaling functions in model Gaussian and large-N problems
and prove their universality with respect to protocol choice. We also introduce
a new protocol in which the critical point is approached asymptotically at late
times with the system marginally out of equilibrium, wherein logarithmic
violations to scaling and anomalous dimensions occur even in the simple
Gaussian problem.Comment: 19 pages,10 figure
Optics with Quantum Hall Skyrmions
A novel type of charged excitation, known as a Skyrmion, has recently been
discovered in quantum Hall systems with filling factor near \nu = 1. A Skyrmion
-- which can be thought of as a topological twist in the spin density of the
electron gas -- has the same charge as an electron, but a much larger spin. In
this review we present a detailed theoretical investigation of the optical
properties of Skyrmions. Our results provide means for the optical detection of
Skyrmions using photoluminescence (PL) spectroscopy. We first consider the
optical properties of Skyrmions in disordered systems. A calculation of the
luminescence energy reveals a special optical signature which allows us to
distinguish between Skyrmions and ordinary electrons. Two experiments to
measure the optical signature are proposed. We then turn to the optical
properties of Skyrmions in pure systems. We show that, just like an ordinary
electron, a Skyrmion may bind with a hole to form a Skyrmionic exciton. The
Skyrmionic exciton can have a lower energy than the ordinary magnetoexciton.
The optical signature of Skyrmions is found to be a robust feature of the PL
spectrum in both disordered and pure systems.Comment: 31 pages, LaTex, 11 eps figures. ijmpb style file included. Review
article submitted to Int. J. Mod. Phys.
Composite bosons in bilayer nu = 1 system: An application of the Murthy-Shankar formalism
We calculate the dispersion of the out-of-phase mode characteristic for the
bilayer nu = 1 quantum Hall system applying the version of Chern-Simons theory
of Murthy and Shankar that cures the unwanted bare electron mass dependence in
the low-energy description of quantum Hall systems. The obtained value for the
mode when d, distance between the layers, is zero is in a good agreement with
the existing pseudospin picture of the system. For d nonzero but small we find
that the mode is linearly dispersing and its velocity to a good approximation
depends linearly on d. This is in agreement with the Hartree-Fock calculations
of the pseudospin picture that predicts a linear dependance on d, and contrary
to the naive Hartree predictions with dependence on the square-root of d. We
set up a formalism that enables one to consider fluctuations around the found
stationary point values. In addition we address the case of imbalanced layers
in the Murthy-Shankar formalism.Comment: 10 pages, 1 figur
Recommended from our members
2016 International Orthoptic Congress Burian Lecture: folklore or evidence?
The theme of the 2016 Burian Lecture is how our understanding of strabismus has been changed by the research carried out in our laboratory in Reading over the years. Accommodation and convergence are fundamental to Orthoptics, but actual responses have often been very different to what we had expected. This paper outlines how our laboratory’s understanding of common issues such as normal development of accommodation and convergence, their linkage, intermittent strabismus, anisometropia, orthoptic exercises and risk factors for strabismus have changed. A new model of thinking about convergence and accommodation may help us to better understand and predict responses in our patients
Dynamics of the Compact, Ferromagnetic \nu=1 Edge
We consider the edge dynamics of a compact, fully spin polarized state at
filling factor . We show that there are two sets of collective
excitations localized near the edge: the much studied, gapless, edge
magnetoplasmon but also an additional edge spin wave that splits off below the
bulk spin wave continuum. We show that both of these excitations can soften at
finite wave-vectors as the potential confining the system is softened, thereby
leading to edge reconstruction by spin texture or charge density wave
formation. We note that a commonly employed model of the edge confining
potential is non-generic in that it systematically underestimates the texturing
instability.Comment: 13 pages, 7 figures, Revte
Solitary Waves of Planar Ferromagnets and the Breakdown of the Spin-Polarized Quantum Hall Effect
A branch of uniformly-propagating solitary waves of planar ferromagnets is
identified. The energy dispersion and structures of the solitary waves are
determined for an isotropic ferromagnet as functions of a conserved momentum.
With increasing momentum, their structure undergoes a transition from a form
ressembling a droplet of spin-waves to a Skyrmion/anti-Skyrmion pair. An
instability to the formation of these solitary waves is shown to provide a
mechanism for the electric field-induced breakdown of the spin-polarized
quantum Hall effect.Comment: 5 pages, 3 eps-figures, revtex with epsf.tex and multicol.st
Low energy excitations of double quantum dots in the lowest Landau level regime
We study the spectrum and magnetic properties of double quantum dots in the
lowest Landau level for different values of the hopping and Zeeman parameters
by means of exact diagonalization techniques in systems of N=6 and N=7
electrons and filling factor close to 2. We compare our results with those
obtained in double quantum layers and single quantum dots. The Kohn theorem is
also discussed.Comment: 23 pages, 4 figures, 1 table; references added; journal versio
Stripes in Quantum Hall Double Layer Systems
We present results of a study of double layer quantum Hall systems in which
each layer has a high-index Landau level that is half-filled. Hartree-Fock
calculations indicate that, above a critical layer separation, the system
becomes unstable to the formation of a unidirectional coherent charge density
wave (UCCDW), which is related to stripe states in single layer systems. The
UCCDW state supports a quantized Hall effect when there is tunneling between
layers, and is {\it always} stable against formation of an isotropic Wigner
crystal for Landau indices . The state does become unstable to the
formation of modulations within the stripes at large enough layer separation.
The UCCDW state supports low-energy modes associated with interlayer coherence.
The coherence allows the formation of charged soliton excitations, which become
gapless in the limit of vanishing tunneling. We argue that this may result in a
novel {\it ``critical Hall state''}, characterized by a power law in
tunneling experiments.Comment: 10 pages, 8 figures include
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