The emptiness formation probability correlation in homogeneous and dimerized XX chains

TL;DR

This paper reviews the properties of the emptiness formation probability in homogeneous and dimerized XX spin chains, analyzing its decay behavior at different temperatures through numerical and analytical methods.

Contribution

It provides a comprehensive numerical analysis of the emptiness formation probability in dimerized XX chains and confirms the decay behavior at various temperatures.

Findings

Exponential decay of correlation at finite temperature in dimerized chains

Gaussian decay of correlation at zero temperature in dimerized chains

Analytical extension of finite temperature behavior to dimerized systems

Abstract

We review some known properties of the "emptiness formation probability" correlation which we have calculated numerically for spin-1/2 XX chains with constant (homogeneous) or alternating (dimerized) nearest-neighbor coupling and an external field (in $z$ direction) for arbitrary temperature. The long-distance asymptotic behavior of this correlation is known to be Gaussian at zero temperature and exponential at finite temperature for the homogeneous chain. By simple analytical arguments the exponential behavior at finite temperature extends to the dimerized system. Numerical results for the dimerized chain confirm the exponential decay at finite temperature and show Gaussian decay at zero temperature.