Full counting statistics and the Edgeworth series for matrix product states

TL;DR

This paper analyzes the full counting statistics of spin in matrix product states, deriving asymptotic corrections to the central limit theorem and examining modifications for topologically nontrivial states like AKLT.

Contribution

It introduces the Edgeworth series approach to quantify finite-size corrections to magnetization distribution in matrix product states.

Findings

Asymptotic corrections to Gaussian distribution are derived.

The approach to Gaussian behavior is modified in topological states like AKLT.

The Edgeworth series effectively describes finite-size effects in spin statistics.

Abstract

We consider full counting statistics of spin in matrix product states. In particular, we study the approach to gaussian distribution for magnetization. We derive the asymptotic corrections to the central limit theorem for magnetization distribution for finite but large blocks in analogy to the Edgeworth series. We also show how central limit theorem like behavior is modified for certain states with topological characteristics such as the AKLT state.