5,763 research outputs found
The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
Among various algorithms designed to exploit the specific properties of
quantum computers with respect to classical ones, the quantum adiabatic
algorithm is a versatile proposition to find the minimal value of an arbitrary
cost function (ground state energy). Random optimization problems provide a
natural testbed to compare its efficiency with that of classical algorithms.
These problems correspond to mean field spin glasses that have been extensively
studied in the classical case. This paper reviews recent analytical works that
extended these studies to incorporate the effect of quantum fluctuations, and
presents also some original results in this direction.Comment: 151 pages, 21 figure
Heterogeneous aging in spin glasses
We introduce a set of theoretical ideas that form the basis for an analytical
framework capable of describing nonequilibrium dynamics in glassy systems. We
test the resulting scenario by comparing its predictions with numerical
simulations of short-range spin glasses. Local fluctuations and responses are
shown to be connected by a generalized local out-of-equilibrium
fluctuation-dissipation relation. Scaling relationships are uncovered for the
slow evolution of heterogeneities at all time scales.Comment: Substantially reorganized to improve clarity of exposition. Accepted
for publication in Physical Review Letters. 5 pages, 4 figure
On the freezing of variables in random constraint satisfaction problems
The set of solutions of random constraint satisfaction problems (zero energy
groundstates of mean-field diluted spin glasses) undergoes several structural
phase transitions as the amount of constraints is increased. This set first
breaks down into a large number of well separated clusters. At the freezing
transition, which is in general distinct from the clustering one, some
variables (spins) take the same value in all solutions of a given cluster. In
this paper we study the critical behavior around the freezing transition, which
appears in the unfrozen phase as the divergence of the sizes of the
rearrangements induced in response to the modification of a variable. The
formalism is developed on generic constraint satisfaction problems and applied
in particular to the random satisfiability of boolean formulas and to the
coloring of random graphs. The computation is first performed in random tree
ensembles, for which we underline a connection with percolation models and with
the reconstruction problem of information theory. The validity of these results
for the original random ensembles is then discussed in the framework of the
cavity method.Comment: 32 pages, 7 figure
Adsorption transition of a self-avoiding polymer chain onto a rigid rod
The subject of this work is the adsorption transition of a long flexible
self-avoiding polymer chain onto a rigid thin rod. The rod is represented by a
cylinder of radius R with a short-ranged attractive surface potential for the
chain monomers. General scaling results are obtained by using renormalization
group arguments in conjunction with available results for quantum field
theories with curved boundaries [McAvity and Osborn 1993 Nucl. Phys. B 394,
728]. Relevant critical exponents are identified and estimated using geometric
arguments.Comment: 19 pages, 4 figures. To appear in: J. Phys.: Condens. Matter, special
issue dedicated to Lothar Schaefer on the occasion of his 60th birthda
Nature of the insulating phases in the half-filled ionic Hubbard model
We investigate the ground-state phase diagram of the one-dimensional "ionic"
Hubbard model with an alternating periodic potential at half-filling by
numerical diagonalization of finite systems with the Lanczos and density matrix
renormalization group (DMRG) methods. We identify an insulator-insulator phase
transition from a band to a correlated insulator with simultaneous charge and
bond-charge order. The transition point is characterized by the vanishing of
the optical excitation gap while simultaneously the charge and spin gaps remain
finite and equal. Indications for a possible second transition into a
Mott-insulator phase are discussed.Comment: final for
Higher order corrections to the effective potential close to the jamming transition in the perceptron model
We analyze the perceptron model performing a Plefka-like expansion of the
free energy. This model falls in the same universality class as hard spheres
near jamming, allowing to get exact predictions in high dimensions for more
complex systems. Our method enables to define an effective potential (or TAP
free energy), namely a coarse-grained functional depending on the contact
forces and the effective gaps between the particles. The derivation is
performed up to the third order, with a particular emphasis on the role of
third order corrections to the TAP free energy. These corrections, irrelevant
in a mean-field framework in the thermodynamic limit, might instead play a
fundamental role when considering finite-size effects. We also study the
typical behavior of the forces and we show that two kinds of corrections can
occur. The first contribution arises since the system is analyzed at a finite
distance from jamming, while the second one is due to finite-size corrections.
In our analysis, third order contributions vanish in the jamming limit, both
for the potential and the generalized forces, in agreement with the argument
proposed by Wyart and coworkers invoking isostaticity. Finally, we analyze the
scalings emerging close to the jamming line, which define a crossover regime
connecting the control parameters of the model to an effective temperature.Comment: 14 pages, 4 figure
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