Asymptotic Behavior of the Emptiness Formation Probability in the Critical Phase of XXZ Spin Chain

TL;DR

This paper investigates the asymptotic decay of the Emptiness Formation Probability in the critical phase of the XXZ spin chain, providing explicit formulas and validating them through numerical simulations.

Contribution

It introduces explicit expressions for the Gaussian decay rate and exponent of EFP in the XXZ chain and confirms their accuracy via numerical methods.

Findings

Derived explicit formulas for EFP decay parameters.

Numerical simulations support the theoretical formulas.

Validated formulas with density-matrix renormalization group and Monte Carlo methods.

Abstract

We study the Emptiness Formation Probability (EFP) for the spin 1/2 XXZ spin chain. EFP P(n) detects a formation of ferromagnetic string of the length n in the ground state. It is expected that EFP decays in a Gaussian way for large strings P(n) ~ n^{-gamma} C^{-n^2}. Here, we propose the explicit expressions for the rate of Gaussian decay C as well as for the exponent gamma. In order to confirm the validity of our formulas, we employed an ab initio simulation technique of the density-matrix renormalization group to simulate XXZ spin chain of sufficient length. Furthermore, we performed Monte-Carlo integration of the Jimbo-Miwa multiple integral for P(n). Those numerical results for P(n) support our formulas fairly definitely.