Publications (2)0 Total impact
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ABSTRACT: This paper deals with fully-connected mean-field models of quantum spins with
p-body ferromagnetic interactions and a transverse field. For p=2 this
corresponds to the quantum Curie-Weiss model (a special case of the
Lipkin-Meshkov-Glick model) which exhibits a second-order phase transition,
while for p>2 the transition is first order. We provide a refined analytical
description both of the static and of the dynamic properties of these models.
In particular we obtain analytically the exponential rate of decay of the gap
at the first-order transition. We also study the slow annealing from the pure
transverse field to the pure ferromagnet (and vice versa) and discuss the
effect of the first-order transition and of the spinodal limit of metastability
on the residual excitation energy, both for finite and exponentially divergent
annealing times. In the quantum computation perspective this quantity would
assess the efficiency of the quantum adiabatic procedure as an approximation
algorithm.
03/2012;
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ABSTRACT: The density of states of disordered hopping models generically exhibits an
essential singularity around the edges of its support, known as a Lifshitz
tail. We study this phenomenon on the Bethe lattice, i.e. for the large-size
limit of random regular graphs, converging locally to the infinite regular
tree, for both diagonal and off-diagonal disorder. The exponential growth of
the volume and surface of balls on these lattices is an obstacle for the
techniques used to characterize the Lifshitz tails in the finite-dimensional
case. We circumvent this difficulty by computing bounds on the moments of the
density of states, and by deriving their implications on the behavior of the
integrated density of states.
04/2011;
