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

TL;DR

This paper investigates energy-filtered quantum states as a means to simulate thermal states, revealing how local indistinguishability coexists with non-local quantum correlations during thermalization.

Contribution

It introduces a protocol for transforming product states into eigenstates with controlled energy variance and identifies three thermalization regimes with distinct local and non-local properties.

Findings

Filtered states mimic time-averaged thermal states locally.

Non-local quantum correlations emerge in medium regimes.

Entanglement entropy scales logarithmically with volume during medium filtering.

Abstract

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. On the other hand, unexpected non-local quantum correlations are generated in the medium regimes and are witnessed by the R\'enyi entanglement entropies of subsystems, which we compute via replica methods. Specifically, two-point correlation functions break cluster decomposition and the entanglement entropy of large regions scales as the logarithm of the volume during the medium filter time.