Density Matrix Renormalization Group Study of Random Dimerized Antiferromagnetic Heisenberg Chains

TL;DR

This study uses the density matrix renormalization group method to analyze how dimerization affects the ground state and string order in random antiferromagnetic Heisenberg chains, revealing the persistence of string order despite randomness.

Contribution

It demonstrates that string long-range order survives in random dimerized chains and provides detailed scaling behaviors of energy and order parameters.

Findings

Ground state energy gain scales as u^a with a > 2

String order persists even with randomness

String order scales as u^{2β} with β ≈ 0.37

Abstract

The effect of dimerization on the random antiferomagnetic Heisenberg chain with spin 1/2 is studied by the density matrix renormalization group method. The ground state energy, the energy gap distribution and the string order parameter are calculated. Using the finite size scaling analysis, the dimerization dependence of the these quantities are obtained. The ground state energy gain due to dimerization behaves as $u^a$ with $a > 2$ where $u$ denotes the degree of dimerization, suggesting the absence of spin-Peierls instability. It is explicitly shown that the string long range order survives even in the presence of randomness. The string order behaves as $u^{2\beta}$ with $\beta \sim 0.37$ in agreement with the recent prediction of real space renormalization group theory ($\beta =(3-\sqrt{5})/2 \simeq 0.382$). The physical picture of this behavior in this model is also discussed.