456 research outputs found
Exactness of the Fock space representation of the q-commutation relations
We show that for all q in the interval (-1,1), the Fock representation of the
q-commutation relations can be unitarily embedded into the Fock representation
of the extended Cuntz algebra. In particular, this implies that the C*-algebra
generated by the Fock representation of the q-commutation relations is exact.
An immediate consequence is that the q-Gaussian von Neumann algebra is weakly
exact for all q in the interval (-1,1).Comment: 20 page
Rank rigidity for CAT(0) cube complexes
We prove that any group acting essentially without a fixed point at infinity
on an irreducible finite-dimensional CAT(0) cube complex contains a rank one
isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube
complexes. We derive a number of other consequences for CAT(0) cube complexes,
including a purely geometric proof of the Tits Alternative, an existence result
for regular elements in (possibly non-uniform) lattices acting on cube
complexes, and a characterization of products of trees in terms of bounded
cohomology.Comment: 39 pages, 4 figures. Revised version according to referee repor
Sequential localization of a complex electron fluid
Complex and correlated quantum systems with promise for new functionality
often involve entwined electronic degrees of freedom. In such materials, highly
unusual properties emerge and could be the result of electron localization.
Here, a cubic heavy fermion metal governed by spins and orbitals is chosen as a
model system for this physics. Its properties are found to originate from
surprisingly simple low-energy behavior, with two distinct localization
transitions driven by a single degree of freedom at a time. This result is
unexpected, but we are able to understand it by advancing the notion of
sequential destruction of an SU(4) spin-orbital-coupled Kondo entanglement. Our
results implicate electron localization as a unified framework for strongly
correlated materials and suggest ways to exploit multiple degrees of freedom
for quantum engineering.Comment: 21 pages, 4 figures (preprint format
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