Sublattice entanglement entropy for fermions

Abstract

In this thesis the entanglement entropy of fermions on sublattices is studied and contrasted with known results for bosons. By studying a $(1+1)$-dimensional periodic lattice and generalizing the notion and theory of circulant matrices to the broader class of phase circulant matrices, the results can be obtained analytically, thus providing a thorough understanding of entanglement entropy of fermion systems. To study the effect of long range coupling, a Lifshitz theory is adapted. To start with, known results for the boson system have been reproduced to provide a background for the fermion results. The results for fermions show, firstly, a significant effect of the boundary conditions on the entanglement entropy. Secondly, a remarkable distinction between massive and massless fermions arises in the result that massless fermions generally have a maximal entanglement entropy. Most striking however, is the insight gained on the effect of long range coupling on the entanglement entropy, where the results for fermions strongly contrast the boson system: the entanglement entropy does not generally increase when long range coupling terms are added. We propose an explanation of this phenomenon by destructive interference. These results provide new and profound insights on entanglement of fermion systems.