# A duality principle for the multi-block entanglement entropy of free fermion systems

## TL;DR

This paper introduces a duality principle for free fermion systems that relates entanglement entropy to dual configurations, leading to a new conjecture for its asymptotic behavior in complex multi-block scenarios.

## Contribution

It establishes a duality principle for entanglement entropy in free fermion systems and formulates a novel conjecture for its asymptotic behavior in multi-block configurations.

## Key findings

- The duality principle accurately predicts entanglement entropy for various configurations.
- The conjecture reproduces numerical results with high precision.
- New asymptotic formulas for mutual and r-partite information are derived.

## Abstract

The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the associated Virasoro algebra. For a free fermion system, the entanglement entropy depends essentially on two sets, namely the set $A$ of sites of the subsystem considered and the set $K$ of excited momentum modes. In this work we make use of a general duality principle establishing the invariance of the entanglement entropy under exchange of the sets $A$ and $K$ to tackle complex problems by studying their dual counterparts. The duality principle is also a key ingredient in the formulation of a novel conjecture for the asymptotic behavior of the entanglement entropy of a free fermion system in the general case in which both sets $A$ and $K$ consist of an arbitrary number of blocks. We have verified that this conjecture reproduces the numerical results with excellent precision for all the configurations analyzed. We have also applied the conjecture to deduce several asymptotic formulas for the mutual and $r$-partite information generalizing the known ones for the single block case.