Quantum Critical Universality and Singular Corner Entanglement Entropy of Bilayer Heisenberg-Ising model

Abstract

We consider a bilayer quantum spin model with anisotropic intra-layer exchange couplings. By varying the anisotropy, the quantum critical phenomena changes from XY to Heisenberg to Ising universality class, with two, three and one modes respectively becoming gapless simultaneously. We use series expansion methods to calculate the second and third Renyi entanglement entropies when the system is bipartitioned into two parts. Leading area-law terms and subleading entropies associated with corners are separately calculated. We find clear evidence that the logarithmic singularity associated with the corners is universal in each class. Its coefficient along the Ising critical line is in excellent agreement with those obtained previously for the transverse-field Ising model. Our results provide strong evidence for the idea that the universal terms in the entanglement entropy provide an approximate measure of the low energy degrees of freedom in the system.