Energy-filtered quantum states and the emergence of non-local correlations

Understand

Energy-filtered quantum states are promising candidates for efficiently simulating thermal states.

• We explore a protocol designed to transition a product state into an eigenstate located in the middle of the spectrum; this is achieved by gradually reducing its energy variance, which allows us to comprehensively understand the crossover phenomenon and the subsequent convergence towards thermal behavior.
• We introduce and discuss three energy-filtering regimes (short, medium and long), and we interpret them as stages of thermalization.
• We show that the properties of the filtered states are locally indistinguishable from those of time-averaged density matrices, routinely employed in the theory of thermalization.