Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices

TL;DR

This study uses quantum Monte Carlo to analyze entanglement entropy in a bilayer Hubbard model, revealing how the antiferromagnetic to singlet transition affects entanglement scaling and highlighting challenges in numerical precision at higher interaction strengths.

Contribution

It applies a recent determinantal quantum Monte Carlo method to compute bipartite Renyi entanglement entropy in a bilayer Hubbard model, comparing different bipartitions and analyzing phase transition signatures.

Findings

Entropy scales as L^2 for one bipartition and linearly with possible logarithmic corrections for the other.

Transition from antiferromagnetic to singlet phase causes entropy saturation.

Numerical uncertainties increase with interaction strength, complicating critical behavior analysis.

Abstract

We calculate the bipartite \Renyi entanglement entropy of an $L\times L\times 2$ bilayer Hubbard model using a determinantal quantum Monte Carlo method recently proposed by Grover [Phys. Rev. Lett. {\bf 111}, 130402 (2013)]. Two types of bipartition are studied: (i) One that divides the lattice into two $L \times L$ planes, and (ii) One that divides the lattice into two equal-size ($L\times L/2\times 2$) bilayers. We compare our calculations with those for the tight-binding model studied by the correlation matrix method. As expected, the entropy for bipartition (i) scales as $L^2$, while the latter scales with $L$ with possible logarithmic corrections. The onset of the antiferromagnet to singlet transition shows up by a saturation of the former to a maximal value and the latter to a small value in the singlet phase. We comment on the large uncertainties in the numerical results with increasing $U$, which would have to be overcome before the critical behavior and logarithmic corrections can be quantified.