Quantum phase transitions in a strongly entangled spin-orbital chain: A field-theoretical approach

TL;DR

This paper investigates quantum phase transitions in a one-dimensional spin-orbital model relevant to vanadium oxides, revealing distinct routes to magnetic order and the role of spin-orbit coupling using a field-theoretical approach.

Contribution

It provides a detailed analysis of the phase diagram and transition types in a coupled spin-orbital chain, highlighting the emergence of Gaussian criticality and the influence of external magnetic fields.

Findings

Long-range Ne9el order appears in the strong coupling limit.

Two distinct routes to Ne9el state depending on energy scales.

Orbital modes can undergo a Gaussian critical transition.

Abstract

Motivated by recent experiments on quasi-1D vanadium oxides, we study quantum phase transitions in a one-dimensional spin-orbital model describing a Haldane chain and a classical Ising chain locally coupled by the relativistic spin-orbit interaction. By employing a field-theoretical approach, we analyze the topology of the ground-state phase diagram and identify the nature of the phase transitions. In the strong coupling limit, a long-range N\'eel order of entangled spin and orbital angular momentum appears in the ground state. We find that, depending on the relative scales of the spin and orbital gaps, the linear chain follows two distinct routes to reach the N\'eel state. First, when the orbital exchange is the dominating energy scale, a two-stage ordering takes place in which the magnetic transition is followed by melting of the orbital Ising order; both transitions belong to the two-dimensional Ising universality class. In the opposite limit, the low-energy orbital modes undergo a continuous reordering transition which represents a line of Gaussian critical points. On this line the orbital degrees of freedom form a Tomonaga-Luttinger liquid. We argue that the emergence of the Gaussian criticality results from merging of the two Ising transitions in the strong hybridization region where the characteristic spin and orbital energy scales become comparable. Finally, we show that, due to the spin-orbit coupling, an external magnetic field acting on the spins can induce an orbital Ising transition.