6,761 research outputs found
Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
We revisit the -pairing states in Hubbard models and explore their
connections to quantum many-body scars to discover a universal scars mechanism.
-pairing occurs due to an algebraic structure known as a Spectrum
Generating Algebra (SGA), giving rise to equally spaced towers of eigenstates
in the spectrum. We generalize the original -pairing construction and
show that several Hubbard-like models on arbitrary graphs exhibit SGAs,
including ones with disorder and spin-orbit coupling. We further define a
Restricted Spectrum Generating Algebra (RSGA) and give examples of
perturbations to the Hubbard-like models that preserve an equally spaced tower
of the original model as eigenstates. The states of the surviving tower exhibit
a sub-thermal entanglement entropy, and we analytically obtain parameter
regimes for which they lie in the bulk of the spectrum, showing that they are
exact quantum many-body scars. The RSGA framework also explains the equally
spaced towers of eigenstates in several well-known models of quantum scars,
including the AKLT model.Comment: 13 pages v2: typos corrected, references adde
Growth of shocked gaseous interfaces in a conical geometry
The results of experiments on Richtmyer-Meshkov instability growth of multimode initial perturbations on an air-sulfur hexafluoride (SF6) interface in a conical geometry are presented. The experiments are done in a relatively larger shock tube. A nominally planar interface is formed by sandwiching a polymeric membrane between wire-mesh frames. A single incident shock wave ruptures the membrane resulting in multimode perturbations. The instability develops from the action of baroclinically deposited vorticity at the interface. The visual thickness delta of the interface is measured from schlieren photographs obtained in each run. Data are presented for delta at times when the interface has become turbulent. The data are compared with the experiments of Vetter [Shock Waves 4, 247 (1995)] which were done in a straight test section geometry, to illustrate the effects of area convergence. It is found from schlieren images that the interface thickness grows about 40% to 50% more rapidly than in Vetter's experiments. Laser induced scattering is used to capture the air-helium interface at late times. Image processing of pictures is also used to determine the interface thickness in cases where it was not clear from the pictures and to obtain the dominant eddy-blob sizes in the mixing zone. Some computational studies are also presented to show the global geometry changes of the interface when it implodes into a conical geometry in both light-heavy and heavy-light cases
Energy Conservation and the Chiral Magnetic Effect
We analyze the chiral magnetic effect in a homogeneous neutral plasma from
the point of view of energy conservation, and construct an effective potential
for the growth of maximally helical perturbations of the electromagnetic field.
We show that a negative curvature at the origin of the potential, indicating
instability of the plasma, is induced by a chiral asymmetry in electron Fermi
energy, as opposed to number density, while the potential grows at large field
value. It follows that the ground state for a plasma has zero magnetic
helicity; a nonzero electron mass will allow an excited state of a plasma with
nonzero helicity to relax to that ground state quickly. We conclude that a
chiral plasma instability triggered by weak interactions is not a viable
mechanism for explaining magnetic fields in stars except possibly when dynamics
drives the system far from equilibrium.Comment: We have corrected a sign error. But the main conclusions of the paper
remain unchange
Maximum Rate of Unitary-Weight, Single-Symbol Decodable STBCs
It is well known that the Space-time Block Codes (STBCs) from Complex
orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol
decodable (SSD). The weight matrices of the square CODs are all unitary and
obtainable from the unitary matrix representations of Clifford Algebras when
the number of transmit antennas is a power of 2. The rate of the square
CODs for has been shown to be complex symbols per
channel use. However, SSD codes having unitary-weight matrices need not be
CODs, an example being the Minimum-Decoding-Complexity STBCs from
Quasi-Orthogonal Designs. In this paper, an achievable upper bound on the rate
of any unitary-weight SSD code is derived to be complex
symbols per channel use for antennas, and this upper bound is larger than
that of the CODs. By way of code construction, the interrelationship between
the weight matrices of unitary-weight SSD codes is studied. Also, the coding
gain of all unitary-weight SSD codes is proved to be the same for QAM
constellations and conditions that are necessary for unitary-weight SSD codes
to achieve full transmit diversity and optimum coding gain are presented.Comment: accepted for publication in the IEEE Transactions on Information
Theory, 9 pages, 1 figure, 1 Tabl
Exact Excited States of Non-Integrable Models
We discuss a method of numerically identifying exact energy eigenstates for a
finite system, whose form can then be obtained analytically. We demonstrate our
method by identifying and deriving exact analytic expressions for several
excited states, including an infinite tower, of the one dimensional spin-1 AKLT
model, a celebrated non-integrable model. The states thus obtained for the AKLT
model can be interpreted as one-to-an extensive number of quasiparticles on the
ground state or on the highest excited state when written in terms of dimers.
Included in these exact states is a tower of states spanning energies from the
ground state to the highest excited state. To our knowledge, this is the first
time that exact analytic expressions for a tower of excited states have been
found in non-integrable models. Some of the states of the tower appear to be in
the bulk of the energy spectrum, allowing us to make conjectures on the strong
Eigenstate Thermalization Hypothesis (ETH). We also generalize these exact
states including the tower of states to the generalized integer spin AKLT
models. Furthermore, we establish a correspondence between some of our states
and those of the Majumdar-Ghosh model, yet another non-integrable model, and
extend our construction to the generalized integer spin AKLT models.Comment: 32 pages, 27 figures v2: References adde
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