Block entanglement and fluctuations in finite size correlated electron systems

TL;DR

This study investigates entanglement entropy and fluctuations in finite correlated electron systems using the Gutzwiller wave function, revealing a metal-insulator crossover and scaling behaviors consistent with conformal field theory predictions.

Contribution

It introduces a scaling form for block entropy in correlated electron systems and links entanglement with spin fluctuations, extending understanding of quantum correlations in finite systems.

Findings

Logarithmic divergence of entanglement entropy for all correlation parameters

Proposed scaling form predicts a metal-insulator crossover at specific system size and correlation

Found a relation between block entropy and bipartite spin fluctuations

Abstract

The block entanglement entropy and fluctuations are investigated in one dimension in finite size correlated electron systems using the Gutzwiller wave function as a prototype correlated electron state. Entanglement entropy shows logarithmic divergence for all values of the correlation projection parameter $g$, as predicted by conformal field theories for critical systems, but the central charge requires finite size corrections. There is an infinite correlation length corresponding to correlation between same kinds of spins, for all values of $g$. A scaling form for the block entropy, as a function of $g$ and the system size $N$, is proposed which predicts a metal-insulator crossover at $N^{1/3} g\approx 0.24$. Bipartite fluctuations in the number of particles in a block, and the spin fluctuations also obey an approximate scaling. A relation is found between the block entropy and the bipartite spin fluctuations. Our results show some correspondence with an experiment on Ni nanochains.