Dimerization transitions in spin-1 chains

TL;DR

This paper investigates phase transitions in a spin-1 chain with complex interactions, revealing conditions for second-order and first-order dimerization transitions and providing numerical evidence for conformal structures.

Contribution

It identifies the universality classes of dimerization transitions in spin-1 chains with additional interactions and demonstrates the role of topological phases and conformal towers.

Findings

Transitions can be second order in SU(2)$_2$ or Ising universality classes.

Numerical evidence of conformal towers of singlets inside the spin gap.

Transitions can also be first-order depending on parameters.

Abstract

We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest neighbor (NNN) and 3-site interactions using extensive numerical simulations and a conformal field theory analysis. We show that the transition can be second order in the WZW SU(2)$_2$ or Ising universality class, or first-order. We argue that these features are generic because of a marginal operator in the WZW SU(2)$_2$ model, and because of two topologically distinct non-dimerized phases with or without edge states. We also provide explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. Implications for other models are briefly discussed.