Spin-Peierls instability in the three-leg Heisenberg ladder

TL;DR

This paper demonstrates that a three-leg Heisenberg ladder undergoes a spin-Peierls transition to a columnar dimerized phase when coupled to phonons, with the state stabilized by spin singlet formation and no quantum criticality.

Contribution

It provides a theoretical prediction of spin-Peierls instability and the resulting dimerized phase in the three-leg Heisenberg ladder using bond-mean-field theory.

Findings

The three-leg ladder exhibits a spin-Peierls transition to a columnar dimerized phase.

The dimerized state is stabilized by spin singlet formation.

No quantum criticality occurs in the columnar dimerized phase.

Abstract

Because the three-leg ladder behaves like a renormalized single Heisenberg chain we argue that a spin-Peierls instability must occur in this system when it is coupled to three-dimensional phonons. Using the bond-mean-field theory, we show that this is indeed the case. The dimerized state below the spin-Peierls transition temperature forms into the columnar dimerized phase not the staggered one. This contrasts with the argument based on antiferromagnetism. A physical argument based rather on spin bonding into singlets explains why the columnar configuration is favored. No quantum criticality (gaplessness) can occur in the columnar arrangement of the dimerized chains.