Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points

TL;DR

This paper investigates the impact of unusual corrections to scaling on the universal properties of Renyi entropies at quantum critical points, emphasizing the importance of accounting for these corrections in numerical analyses.

Contribution

It reveals the significance of unusual corrections to scaling in Renyi entropies and proposes a two-step extrapolation method to accurately determine universal properties.

Findings

Unusual corrections grow with increasing Renyi index.

Ignoring corrections can lead to qualitatively incorrect critical exponents.

Correct accounting of corrections yields accurate universal quantities.

Abstract

At a quantum critical point, bipartite entanglement entropies have universal quantities which are subleading to the ubiquitous area law. For Renyi entropies, these terms are known to be similar to the von Neumann entropy, while being much more amenable to numerical and even experimental measurement. We show here that when calculating universal properties of Renyi entropies, it is important to account for unusual corrections to scaling that arise from relevant local operators present at the conical singularity in the multi-sheeted Riemann surface. These corrections grow in importance with increasing Renyi index. We present studies of Renyi correlation functions in the 1+1 transverse-field Ising model (TFIM) using conformal field theory, mapping to free fermions, and series expansions, and the logarithmic entropy singularity at a corner in 2+1 for both free bosonic field theory and the TFIM, using numerical linked cluster expansions. In all numerical studies, accurate results are only obtained when unusual corrections to scaling are taken into account. In the worst case, an analysis ignoring these corrections can get qualitatively incorrect answers, such as predicting a decrease in critical exponents with the Renyi index, when they are actually increasing. We discuss a two-step extrapolation procedure that can be used to account for the unusual corrections to scaling.