Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice

TL;DR

This study computes the universal shape dependence of two-cylinder Renyi entropies for free bosons on finite lattices, comparing numerical results with continuum theories to understand quantum critical points.

Contribution

It provides exact lattice calculations of two-cylinder entanglement entropies and compares them with continuum ansatzes, including AdS/CFT and Lifshitz models, revealing good agreement.

Findings

Numerical fits align well with continuum functions from AdS/CFT and Lifshitz models.

Universal scalars in the thin-cylinder limit match continuum free boson theory values.

Lattice calculations validate continuum approximations for entanglement entropy shape dependence.

Abstract

Universal scaling terms occurring in Renyi entanglement entropies have the potential to bring new understanding to quantum critical points in free and interacting systems. Quantitative comparisons between analytical continuum theories and numerical calculations on lattice models play a crucial role in advancing such studies. In this paper, we exactly calculate the universal two-cylinder shape dependence of entanglement entropies for free bosons on finite-size square lattices, and compare to approximate functions derived in the continuum using several different ansatzes. Although none of these ansatzes are exact in the thermodynamic limit, we find that numerical fits are in good agreement with continuum functions derived using the AdS/CFT correspondence, an extensive mutual information model, and a quantum Lifshitz model. We use fits of our lattice data to these functions to calculate universal scalars defined in the thin-cylinder limit, and compare to values previously obtained for the free boson field theory in the continuum.