Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor

Abstract

We study a model of two dimensional, topological superconductivity on a square lattice. The model contains hopping, spin orbit coupling and a time reversal symmetry breaking Zeeman term. This term, together with the chemical potential act as knobs that induce transitions between trivial and topological superconductivity. As previously found numerically, the transitions are seen in the entanglement entropy as cusps as a function of model parameters. In this work we study the entanglement entropy analytically by keeping only its most important components. Our study is based on the intuition that the number of Fermi surfaces in the system controls the topological invariant. With our approximate expression for the entanglement entropy we are able to extract the divergent entanglement entropy derivative close to the phase transition.

6 pages, 3 figures

References in corpus (15)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number
• Measuring entanglement using quantum quenches
• Towards measuring Entanglement Entropies in Many Body Systems
• Multipartite Entangled Spatial Modes of Ultracold Atoms Generated and Controlled by Quantum Measurement
• Entanglement entropy in dynamic quantum-coherent conductors
• Subarea law of entanglement in nodal fermionic systems
• Scaling of entanglement entropy across Lifshitz transitions
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Entanglement Spectrum as a Probe for the Topology of a Spin-Orbit Coupled Superconductor
• Entanglement Spectrum of a Random Partition: Connection with the Localization Transition
• Effect of Single Impurity on Free Fermion Entanglement Entropy

Cited by in corpus (2)

• Flat bands and entanglement in the Kitaev ladder
• Disorder induced topological phase transition in a driven Majorana chain