Equipartition of the Entanglement Entropy

TL;DR

This paper investigates how entanglement entropy is distributed among sectors in U(1)-symmetric quantum systems, revealing equal distribution and providing a new method to estimate critical properties like the central charge.

Contribution

It demonstrates that entanglement entropy is equally partitioned among sectors and introduces a simple numerical method to estimate central charge and critical exponents.

Findings

Entanglement entropy is equally distributed among sectors.

The entropy follows a logarithmic law with a double logarithmic correction.

The method accurately estimates the central charge c for the XXZ chain.

Abstract

The entanglement in a quantum system that possess an internal symmetry, characterized by the Sz-magnetization or U(1)-charge, is distributed among different sectors. The aim of this letter is to gain a deeper understanding of the contribution to the entanglement entropy in each of those sectors for the ground state of conformal invariant critical one dimensional systems. We find surprisingly that the entanglement entropy is equally distributed among the different magnetization sectors. Its value is given by the standard area law violating logarithmic term, that depends on the central charge c, minus a double logarithmic correction related to the zero temperature susceptibility. This result provides a new method to estimate simultaneously the central charge c and the critical exponents of U(1)-symmetric quantum chains. The method is numerically simple and gives precise results for the spin-1/2 quantum XXZ chain. We also compute the probability distribution of the magnetization in contiguous sublattices.