Nonequilibrium power-law correlations in a system of tight-binding fermions with gapped spectrum

A quantum quench is explored in a system of tight-binding fermions in which a smooth, linearly-varying chemical potential is rapidly switched off at the same time a staggered chemical potential is turned on. The initial particle density profile is a ``domain wall'' shape and evolves unitarily under a Hamiltonian which possesses a gap in its spectrum. In the ground-state of the Hamiltonian generating time evolution, correlations decay exponentially with distance, while in this non-equilibrium setting, a steady state quickly forms within a central subsystem in which power-law correlations persist. The long-time average of the particle density, current and various correlation functions are shown to be obtainable from an effective momentum distribution which depends on the details of the Hamiltonian and the initial state. Intriguing similarities between the results in this model of free fermions and similar results obtained within interacting systems are discussed.