A numerical study of the Random Dimerized XX spin-1/2 chain

TL;DR

This study investigates how randomness and dimerization influence the spin-1/2 XX chain, confirming theoretical predictions for correlation decay and providing larger-scale numerical results than previous research.

Contribution

It offers a comprehensive numerical analysis of the random dimerized XX chain, validating RG predictions and exploring crossover behaviors with larger system sizes.

Findings

Correlation decay exponents match RG predictions

Cross-over functions for the dimer phase are presented

Disorder averages for larger systems up to N=1024

Abstract

The effects of randomness and dimerization on the spin-1/2 XX chain are studied by a mapping to free fermions. Results are presented for the transverse and longitudinal components of the average and typical spin and string correlation functions. Contrary to previous numerical evidence, the decay exponents of all the above correlation functions are found to be in good agreement with the theoretical RG predictions for the random singlet phase. We also present cross-over functions for the above correlation functions in the random dimer phase. Disorder averages have been taken for system sizes up to N=1024, about ten times larger than in previous studies.