7,750 research outputs found
Gravity Dual of a Quantum Hall Plateau Transition
We show how to model the transition between distinct quantum Hall plateaus in
terms of D-branes in string theory. A low energy theory of 2+1 dimensional
fermions is obtained by considering the D3-D7 system, and the plateau
transition corresponds to moving the branes through one another. We study the
transition at strong coupling using gauge/gravity duality and the probe
approximation. Strong coupling leads to a novel kind of plateau transition: at
low temperatures the transition remains discontinuous due to the effects of
dynamical symmetry breaking and mass generation, and at high temperatures is
only partially smoothed out.Comment: 27 pages, 6 figures, harvmac; v2, references and minor comments
added, version to be submitted to JHEP; v3, corrections to section
On the Geroch-Traschen class of metrics
We compare two approaches to semi-Riemannian metrics of low regularity. The maximally 'reasonable' distributional setting of Geroch and Traschen is shown to be consistently contained in the more general setting of nonlinear distributional geometry in the sense of Colombea
A Holographic Quantum Critical Point at Finite Magnetic Field and Finite Density
We analyze the phase diagram of N=4 supersymmetric Yang-Mills theory with
fundamental matter in the presence of a background magnetic field and nonzero
baryon number. We identify an isolated quantum critical point separating two
differently ordered finite density phases. The ingredients that give rise to
this transition are generic in a holographic setup, leading us to conjecture
that such critical points should be rather common. In this case, the quantum
phase transition is second order with mean-field exponents. We characterize the
neighborhood of the critical point at small temperatures and identify some
signatures of a new phase dominated by the critical point. We also identify the
line of transitions between the finite density and zero density phases. The
line is completely determined by the mass of the lightest charged quasiparticle
at zero density. Finally, we measure the magnetic susceptibility and find hints
of fermion condensation at large magnetic field.Comment: 29 pages, 8 figure
On the Burer-Monteiro method for general semidefinite programs
Consider a semidefinite program (SDP) involving an positive
semidefinite matrix . The Burer-Monteiro method uses the substitution to obtain a nonconvex optimization problem in terms of an
matrix . Boumal et al. showed that this nonconvex method provably solves
equality-constrained SDPs with a generic cost matrix when , where is the number of constraints. In this note we extend
their result to arbitrary SDPs, possibly involving inequalities or multiple
semidefinite constraints. We derive similar guarantees for a fixed cost matrix
and generic constraints. We illustrate applications to matrix sensing and
integer quadratic minimization.Comment: 10 page
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