Quantum Criticality in Dimerized Spin Ladders

TL;DR

This paper investigates quantum criticality in dimerized spin ladders, revealing that only staggered dimerization patterns can exhibit criticality, while columnar patterns remain gapped, with findings supported by bond mean-field theory and numerical results.

Contribution

It introduces analysis of different dimerization patterns in spin ladders, showing that only staggered dimerization leads to quantum criticality, contrasting with previous studies focused on uniform patterns.

Findings

Columnar dimerization results in gapped ladders with lower energy.

Staggered dimerization exhibits quantum critical lines.

Bond mean-field theory aligns with numerical results.

Abstract

We analyze a possibility of quantum criticality (gaplessness) in dimerized antiferromagnetic two- and three-leg spin-1/2 ladders. Contrary to earlier studies of these models, we examine different dimerization patterns in the ladder. We find that ladders with the columnar dimerization order have lower zero-temperature energies and they are always gapped. For the staggered dimerization order, we find the quantum critical lines, in agreement with earlier analyses. The bond mean-field theory we apply, demonstrates its quantitative accuracy and agrees with available numerical results. We conclude that unless some mechanism for locking dimerization into the energetically less favorable staggered configuration is provided, the dimerized ladders do not order into the phase where the quantum criticality occurs.