Entropy perspective on the thermal crossover in a fermionic Hubbard chain

We study the Renyi entropy in the finite-temperature crossover regime of a Hubbard chain using quantum Monte Carlo. The ground-state entropy has characteristic features such as a logarithmic divergence with block size and $2{k}_{\mathrm{F}}$ oscillations that are a hallmark of its Luttinger liquid nature. The interplay between the (extensive) thermal entropy and the ground-state features is studied and we analyze the temperature-induced decay of the amplitude of the oscillations as well as the scaling of the purity. Furthermore, we show how the spin and charge velocities can be extracted from the temperature dependence of the Renyi entropy, bridging our findings to recent experimental proposals on how to implement the measurement of Renyi entropies in the cold atom system. Studying the Renyi mutual information, we also demonstrate how constraints such as particle number conservation can induce persistent correlations visible in the mutual information even at high temperature.