  We present a modification of the Hybrid Monte Carlo algorithm for tackling
the critical slowing down of generating Markov chains of lattice gauge
configurations towards the continuum limit. We propose a new method to exchange
information within an ensemble of Markov chains, and use it to construct an
approximate inverse Hessian matrix of the action inspired from quasi-Newton
algorithms for optimization. The kinetic term of the molecular dynamics
evolution includes the approximate Hessian for long distance couplings among
the momenta. We show the result of applying the new algorithm to the $U(1)$
gauge theory in two dimensions, and discuss our future plans.
