Criticality in statistical physics naturally emerges at isolated points in the phase diagram. Jamming of spheres is not an exception: varying density, it is the critical point that separates the unjammed phase where spheres do not overlap and the jammed phase where they cannot be arranged without overlaps. The same remains true in more general constraint satisfaction problems with continuous variables (CCSP) where jamming coincides with the (protocol dependent) satisfiability transition point. In this work we show that by carefully choosing the cost function to be minimized, the region of criticality extends to occupy a whole region of the jammed phase. As a working example, we consider the spherical perceptron with a linear cost function in the unsatisfiable (UNSAT) jammed phase and we perform numerical simulations which show critical power laws emerging in the configurations obtained minimizing the linear cost function. We develop a scaling theory to compute the emerging critical exponents.

We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field H = H(sin theta cos phi, sin theta sin phi cos theta) induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for alpha < 1. We report a divergence of the Berry curvature at alpha(c) = 1 for magnetic fields aligned along the equator theta = pi/2. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs at the localization Kosterlitz-Thouless quantum phase transition in this model. Recent experiments in quantum circuits have engineered nonequilibrium protocols to access topological properties from a measurement of a dynamical Chern number defined via the out-of-equilibrium spin expectation values. Applying a numerically exact stochastic Schrodinger approach we find that, for a fixed field sweep velocity theta(t) = vt, the bath induces a crossover from ( quasi) adiabatic to nonadiabatic dynamical behavior when the spin bath coupling a increases. We also investigate the particular regime H/omega(c) << v/H << 1 with large bath cutoff frequency.c, where the dynamical Chern number vanishes already at alpha = 1/2. In this regime, the mapping to an interacting resonance level model enables us to analytically describe the behavior of the dynamical Chern number in the vicinity of alpha = 1/2. We further provide an intuitive physical explanation of the bath-induced breakdown of adiabaticity in analogy to the Faraday effect in electromagnetism. We demonstrate that the driving of the spin leads to the production of a large number of bosonic excitations in the bath, which strongly affect the spin dynamics. Finally, we quantify the spin-bath entanglement and formulate an analogy with an effective model at thermal equilibrium. Disciplines Condensed Matter Physics | Physics CommentsThis article is published as Henriet, Loïc, Antonio Sclocchi, Peter P. Orth, and Karyn Le Hur. "Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect." Physical Review B 95, no. 5 (2017) We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field H = H (sin θ cos φ, sin θ sin φ, cos θ ) induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for α < 1. We report a divergence of the Berry curvature at α c = 1 for magnetic fields aligned along the equator θ = π/2. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs a...