2,536 research outputs found
Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States
We conjecture that the counting of the levels in the orbital entanglement
spectra (OES) of finite-sized Laughlin Fractional Quantum Hall (FQH) droplets
at filling is described by the Haldane statistics of particles in a
box of finite size. This principle explains the observed deviations of the OES
counting from the edge-mode conformal field theory counting and directly
provides us with a topological number of the FQH states inaccessible in the
thermodynamic limit- the boson compactification radius. It also suggests that
the entanglement gap in the Coulomb spectrum in the conformal limit protects a
universal quantity- the statistics of the state. We support our conjecture with
ample numerical checks.Comment: 4.1 pages, published versio
Bulk-Edge Correspondence in the Entanglement Spectra
Li and Haldane conjectured and numerically substantiated that the
entanglement spectrum of the reduced density matrix of ground-states of
time-reversal breaking topological phases (fractional quantum Hall states)
contains information about the counting of their edge modes when the
ground-state is cut in two spatially distinct regions and one of the regions is
traced out. We analytically substantiate this conjecture for a series of FQH
states defined as unique zero modes of pseudopotential Hamiltonians by finding
a one to one map between the thermodynamic limit counting of two different
entanglement spectra: the particle entanglement spectrum, whose counting of
eigenvalues for each good quantum number is identical (up to accidental
degeneracies) to the counting of bulk quasiholes, and the orbital entanglement
spectrum (the Li-Haldane spectrum). As the particle entanglement spectrum is
related to bulk quasihole physics and the orbital entanglement spectrum is
related to edge physics, our map can be thought of as a mathematically sound
microscopic description of bulk-edge correspondence in entanglement spectra. By
using a set of clustering operators which have their origin in conformal field
theory (CFT) operator expansions, we show that the counting of the orbital
entanglement spectrum eigenvalues in the thermodynamic limit must be identical
to the counting of quasiholes in the bulk. The latter equals the counting of
edge modes at a hard-wall boundary placed on the sample. Moreover, we show this
to be true even for CFT states which are likely bulk gapless, such as the
Gaffnian wavefunction.Comment: 20 pages, 6 figure
Real-Space Entanglement Spectrum of Quantum Hall States
We investigate the entanglement spectra arising from sharp real-space
partitions of the system for quantum Hall states. These partitions differ from
the previously utilized orbital and particle partitions and reveal
complementary aspects of the physics of these topologically ordered systems. We
show, by constructing one to one maps to the particle partition entanglement
spectra, that the counting of the real-space entanglement spectra levels for
different particle number sectors versus their angular momentum along the
spatial partition boundary is equal to the counting of states for the system
with a number of (unpinned) bulk quasiholes excitations corresponding to the
same particle and flux numbers. This proves that, for an ideal model state
described by a conformal field theory, the real-space entanglement spectra
level counting is bounded by the counting of the conformal field theory edge
modes. This bound is known to be saturated in the thermodynamic limit (and at
finite sizes for certain states). Numerically analyzing several ideal model
states, we find that the real-space entanglement spectra indeed display the
edge modes dispersion relations expected from their corresponding conformal
field theories. We also numerically find that the real-space entanglement
spectra of Coulomb interaction ground states exhibit a series of branches,
which we relate to the model state and (above an entanglement gap) to its
quasiparticle-quasihole excitations. We also numerically compute the
entanglement entropy for the nu=1 integer quantum Hall state with real-space
partitions and compare against the analytic prediction. We find that the
entanglement entropy indeed scales linearly with the boundary length for large
enough systems, but that the attainable system sizes are still too small to
provide a reliable extraction of the sub-leading topological entanglement
entropy term.Comment: 13 pages, 11 figures; v2: minor corrections and formatting change
Turbulence and Mixing in the Intracluster Medium
The intracluster medium (ICM) is stably stratified in the hydrodynamic sense
with the entropy increasing outwards. However, thermal conduction along
magnetic field lines fundamentally changes the stability of the ICM, leading to
the "heat-flux buoyancy instability" when and the "magnetothermal
instability" when . The ICM is thus buoyantly unstable regardless of
the signs of and . On the other hand, these
temperature-gradient-driven instabilities saturate by reorienting the magnetic
field (perpendicular to when and parallel to when ), without generating sustained convection. We show that
after an anisotropically conducting plasma reaches this nonlinearly stable
magnetic configuration, it experiences a buoyant restoring force that resists
further distortions of the magnetic field. This restoring force is analogous to
the buoyant restoring force experienced by a stably stratified adiabatic
plasma. We argue that in order for a driving mechanism (e.g, galaxy motions or
cosmic-ray buoyancy) to overcome this restoring force and generate turbulence
in the ICM, the strength of the driving must exceed a threshold, corresponding
to turbulent velocities . For weaker driving, the ICM
remains in its nonlinearly stable magnetic configuration, and turbulent mixing
is effectively absent. We discuss the implications of these findings for the
turbulent diffusion of metals and heat in the ICM.Comment: 8 pages, 2 figs., submitted to the conference proceedings of "The
Monster's Fiery Breath;" a follow up of arXiv:0901.4786 focusing on the
general mixing properties of the IC
Fracture toughness of two Cr2Hf+Cr intermetallic composites as a function temperature
Journal ArticleFracture toughness as a function of temperature was evaluated for two Cr2Hf+Cr intermetallic composites, each in two different microstructural conditions. The proeutectic microstructures based on Cr-6.5Hf (at%) showed a significant increase in fracture toughness with an increase from room temperature to 600°C
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