Second-order Peierls transition in the spin-orbital Kumar-Heisenberg model

TL;DR

This paper investigates the effects of adding a Heisenberg interaction to a spin-orbital model, revealing a second-order phase transition and dimerization phenomena at small coupling, and identifying another phase transition at large coupling.

Contribution

It introduces and analyzes the impact of a Heisenberg term on the Kumar spin-orbital model, uncovering a second-order phase transition and detailed phase behavior in different limits.

Findings

Finite Heisenberg interaction induces spontaneous dimerization.

Phase transition at small coupling is smooth (second order).

Another phase transition occurs at large coupling, with analytical explanations.

Abstract

We add a Heisenberg interaction term $\propto\lambda$ in the one-dimensional SU(2)$\otimes$XY spin-orbital model introduced by B. Kumar. At $\lambda=0$ the spin and orbital degrees of freedom can be separated by a unitary transformation leading to an exact solution of the model. We show that a finite $\lambda>0$ leads to spontaneous dimerization of the system which in the thermodynamic limit becomes a smooth phase transition at $\lambda\to 0$, whereas it remains discontinuous within the first order perturbation approach. We present the behavior of the entanglement entropy, energy gap and dimerization order parameter in the limit of $\lambda\to 0$ confirming the critical behavior. Finally, we show the evidence of another phase transition in the Heisenberg limit, $\lambda\to\infty$, and give a qualitative analytical explanation of the observed dimerized states both in the limit of small and large $\lambda$.