Random Bonds and Topological Stability in Gapped Quantum Spin Chains

TL;DR

This paper investigates how random bonds affect gapped quantum spin chains, revealing that topological order persists despite disorder and that dimerization influences the phase behavior, with implications for the stability of topological phases.

Contribution

It demonstrates that topological order remains stable under randomness and dimerization in quantum spin chains, providing new insights into disorder effects on topological phases.

Findings

Dimerization is relevant at the random singlet fixed point.

Dimerized chains exhibit Griffiths phase with divergent susceptibility.

Topological string order is preserved despite bond randomness.

Abstract

We study the effects of random bonds on spin chains that have an excitation gap in the absence of randomness. The dimerized spin-1/2 chain is our principal example. Using an asymptotically exact real space decimation renormalization group procedure, we find that dimerization is a relevant perturbation at the random singlet fixed point. For weak dimerization, the dimerized chain is in a Griffiths phase with short range spin-spin correlations and a divergent susceptibility. The string topological order, however, is not destroyed by bond randomness and dimerization is stabilized by the confinement of topological defects. We conjecture that random integer spin chains in the Haldane phase exhibit similar thermodynamic and topological properties.