548 research outputs found
Design concept for pressure switch calibrator
Calibrator and switch design enables pressure switches to operate under 150 g shock loads. The design employs a saturated liquid-to-vapor phase transition at constant pressure to produce a known force independent of displacement over a usable range
Topological Blocking in Quantum Quench Dynamics
We study the non-equilibrium dynamics of quenching through a quantum critical
point in topological systems, focusing on one of their defining features:
ground state degeneracies and associated topological sectors. We present the
notion of 'topological blocking', experienced by the dynamics due to a mismatch
in degeneracies between two phases and we argue that the dynamic evolution of
the quench depends strongly on the topological sector being probed. We
demonstrate this interplay between quench and topology in models stemming from
two extensively studied systems, the transverse Ising chain and the Kitaev
honeycomb model. Through non-local maps of each of these systems, we
effectively study spinless fermionic -wave paired superconductors. Confining
the systems to ring and toroidal geometries, respectively, enables us to
cleanly address degeneracies, subtle issues of fermion occupation and parity,
and mismatches between topological sectors. We show that various features of
the quench, which are related to Kibble-Zurek physics, are sensitive to the
topological sector being probed, in particular, the overlap between the
time-evolved initial ground state and an appropriate low-energy state of the
final Hamiltonian. While most of our study is confined to translationally
invariant systems, where momentum is a convenient quantum number, we briefly
consider the effect of disorder and illustrate how this can influence the
quench in a qualitatively different way depending on the topological sector
considered.Comment: 18 pages, 11 figure
Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
We describe a family of phase transitions connecting phases of differing
non-trivial topological order by explicitly constructing Hamiltonians of the
Levin-Wen[PRB 71, 045110] type which can be tuned between two solvable points,
each of which realizes a different topologically ordered phase. We show that
the low-energy degrees of freedom near the phase transition can be mapped onto
those of a Potts model, and we discuss the stability of the resulting phase
diagram to small perturbations about the model. We further explain how the
excitations in the condensed phase are formed from those in the original
topological theory, some of which are split into multiple components by
condensation, and we discuss the implications of our results for understanding
the nature of general achiral topological phases in 2+1 dimensions in terms of
doubled Chern-Simons theories
Exact results for the star lattice chiral spin liquid
We examine the star lattice Kitaev model whose ground state is a a chiral
spin liquid. We fermionize the model such that the fermionic vacua are toric
code states on an effective Kagome lattice. This implies that the Abelian phase
of the system is inherited from the fermionic vacua and that time reversal
symmetry is spontaneously broken at the level of the vacuum. In terms of these
fermions we derive the Bloch-matrix Hamiltonians for the vortex free sector and
its time reversed counterpart and illuminate the relationships between the
sectors. The phase diagram for the model is shown to be a sphere in the space
of coupling parameters around the triangles of the lattices. The abelian phase
lies inside the sphere and the critical boundary between topologically distinct
Abelian and non-Abelian phases lies on the surface. Outside the sphere the
system is generically gapped except in the planes where the coupling parameters
are zero. These cases correspond to bipartite lattice structures and the
dispersion relations are similar to that of the original Kitaev honeycomb
model. In a further analysis we demonstrate the three-fold non-Abelian
groundstate degeneracy on a torus by explicit calculation.Comment: 7 pages, 8 figure
Josephson-coupled Moore-Read states
We study a quantum Hall bilayer system of bosons at total filling factor ν = 1, and study the phase that results from short ranged pair-tunneling combined with short ranged interlayer interactions. We introduce two exactly solvable model Hamiltonians which both yield the coupled Moore-Read state [Phys. Rev. Lett. 108, 256809 (2012)] as a ground state, when projected onto fixed particle numbers in each layer. One of these Hamiltonians describes a gapped topological phase while the other is gapless. However, on introduction of a pair tunneling term, the second system becomes gapped and develops the same topological order as the gapped Hamiltonian. Supported by the exact solution of the full zero-energy quasihole spectrum and a conformal field theory approach, we develop an intuitive picture of this system as two coupled composite fermion superconductors. In this language, pair tunneling provides a Josephson coupling of the superconducting phases of the two layers, and gaps out the Goldstone mode associated with particle transport between the layers. In particular, this implies that quasiparticles are confined between the layers. In the bulk, the resulting phase has the topological order of the Halperin 220 phase with U(1)_2 x U(1)_2 topological order, but it is realized in the symmetric/antisymmetric-basis of the layer index. Consequently, the edge spectrum at a fixed particle number reveals an unexpected U(1)_4 x U(1) structure.The authors would like to thank Nordita and the Aspen Center for Physics their hospitality, and acknowledge
support from the Leverhulme Trust under grant ECF-2011-565, the Newton Trust of the University
of Cambridge and by the Royal Society under grant UF120157 (G.M.), the European Union under
Marie Curie award 299890 QETPM (L.H.), Science Foundation Ireland principal investigator awards
08/IN.1/I1961 and 12/IA/1697 (J.K.S.) and EPSRC grant EP/I032487/1 (S.H.S.).This is the author accepted version of the manuscript which has been published at http://dx.doi.org/10.1103/PhysRevB.90.23510
Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model
The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost
Clebsch-Gordan and 6j-coefficients for rank two quantum groups
We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two
quantum groups. We explain in detail how such calculations are done, which
should allow the reader to perform similar calculations in other cases.
Moreover, we tabulate the q-Clebsch-Gordan and 6j-coefficients explicitly, as
well as some other topological data associated with theories corresponding to
rank-two quantum groups. Finally, we collect some useful properties of the
fusion rules of particular conformal field theories.Comment: 43 pages. v2: minor changes and added references. For mathematica
notebooks containing the various q-CG and 6j symbols, see
http://arxiv.org/src/1004.5456/an
The modular S-matrix as order parameter for topological phase transitions
We study topological phase transitions in discrete gauge theories in two
spatial dimensions induced by the formation of a Bose condensate. We analyse a
general class of euclidean lattice actions for these theories which contain one
coupling constant for each conjugacy class of the gauge group. To probe the
phase structure we use a complete set of open and closed anyonic string
operators. The open strings allow one to determine the particle content of the
condensate, whereas the closed strings enable us to determine the matrix
elements of the modular -matrix, also in the broken phase. From the measured
broken -matrix we may read off the sectors that split or get identified in
the broken phase, as well as the sectors that are confined. In this sense the
modular -matrix can be employed as a matrix valued non-local order parameter
from which the low-energy effective theories that occur in different regions of
parameter space can be fully determined.
To verify our predictions we studied a non-abelian anyon model based on the
quaternion group of order eight by Monte Carlo simulation. We
probe part of the phase diagram for the pure gauge theory and find a variety of
phases with magnetic condensates leading to various forms of (partial)
confinement in complete agreement with the algebraic breaking analysis. Also
the order of various transitions is established.Comment: 37 page
Topological Qubit Design and Leakage
We examine how best to design qubits for use in topological quantum
computation. These qubits are topological Hilbert spaces associated with small
groups of anyons. Op- erations are performed on these by exchanging the anyons.
One might argue that, in order to have as many simple single qubit operations
as possible, the number of anyons per group should be maximized. However, we
show that there is a maximal number of particles per qubit, namely 4, and more
generally a maximal number of particles for qudits of dimension d. We also look
at the possibility of having topological qubits for which one can perform
two-qubit gates without leakage into non-computational states. It turns out
that the requirement that all two-qubit gates are leakage free is very
restrictive and this property can only be realized for two-qubit systems
related to Ising-like anyon models, which do not allow for universal quantum
computation by braiding. Our results follow directly from the representation
theory of braid groups which means they are valid for all anyon models. We also
make some remarks on generalizations to other exchange groups.Comment: 13 pages, 3 figure
Fluvio-deltaic avulsions during relative sea-level fall.
Understanding river response to changes in relative sea level (RSL) is essential for predicting fluvial stratigraphy and source-to-sink dynamics. Recent theoretical work has suggested that rivers can remain aggradational during RSL fall, but field data are needed to verify this response and investigate sediment deposition processes. We show with field work and modeling that fluvio-deltaic systems can remain aggradational or at grade during RSL fall, leading to superelevation and continuation of delta lobe avulsions. The field site is the Goose River, Newfoundland-Labrador, Canada, which has experienced steady RSL fall of around 3–4 mm yr⁻¹ in the past 5 k.y. from post-glacial isostatic rebound. Elevation analysis and optically stimulated luminescence dating suggest that the Goose River avulsed and deposited three delta lobes during RSL fall. Simulation results from Delft3D software show that if the characteristic fluvial response time is longer than the duration of RSL fall, then fluvial systems remain aggradational or at grade, and continue to avulse during RSL fall due to superelevation. Intriguingly, we find that avulsions become more frequent at faster rates of RSL fall, provided the system response time remains longer than the duration of RSL fall. This work suggests that RSL fall rate may influence the architecture of falling-stage or forced regression deposits by controlling the number of deposited delta lobes
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