Dimensionality-Changing Transition from a Non-Fermi Liquid to a Spin-Solid in a Multichannel Kondo Lattice

One of the simplest realizations of a zero-dimensional non-Fermi liquid arises in the overscreened regime of the multichannel Kondo model, where a single quantum spin couples to K>1 channels of conduction electrons. We investigate the fate of a Heisenberg chain of SU(N) multichannel quantum dots, where each spin is coupled to its own electronic bath with K channels. A simple renormalization group argument shows that the spins dynamically decouple at low energies when N>K, giving rise to a ``sliding'' non-Fermi liquid phase. Quantum Monte Carlo simulations reveal the existence of a valence-bond-solid phase at strong Heisenberg coupling and a continuous ``dimensionality-changing'' transition between these two phases. Remarkably, at the critical point, correlations exhibit a power-law decay even along the chain direction, signaling the breakdown of dynamical decoupling. We further develop a renormalization group framework that captures the universal aspects of this critical point.