Entanglement Entropy in Many-Fermion System

TL;DR

This paper explores entanglement entropy in many-fermion systems, reviewing recent developments, calculating it in various models, and proposing bosonization as a tool for high-dimensional analysis.

Contribution

It introduces a comprehensive approach to studying entanglement entropy across different dimensions and systems, connecting fermionic and bosonic models through bosonization techniques.

Findings

Entanglement entropy calculated in 1D fermionic and bosonic systems.

Connection established between fermionic and bosonic models via bosonization.

Discussion on extending bosonization to high-dimensional systems.

Abstract

In this four-part prospectus, we first give a brief introduction to the motivation for studying entanglement entropy and some recent development. Then follows a summary of our recent work about entanglement entropy in states with traditional long-range order. After that we demonstrate calculation of entanglement entropy in both one-dimensional spin-less fermionic systems as well as bosonic systems via different approaches, and connect them using one-dimensional bosonization. In the last part, we briefly sketch the idea of bosonization in high-dimensions, and discuss the possibility and advantage of approaching the scaling behavior of entanglement entropy of fermions in arbitrary dimensions via bosonization.