Quantum criticality of vanadium chains with strong relativistic spin-orbit interaction

TL;DR

This paper investigates quantum phase transitions in vanadium chains caused by spin-orbit interactions, revealing a complex phase diagram with distinct ordered states and transitions, using analytical and numerical methods.

Contribution

It introduces a detailed analysis of the quantum critical behavior in vanadium chains with strong spin-orbit coupling, highlighting an intermediate phase with combined order.

Findings

Identification of an intermediate phase with ferro-orbital and spin Neel order

Boundaries of phases determined by Ising transition lines

Implications for specific vanadium compounds CaV2O4 and ZnV2O4

Abstract

We study quantum phase transitions induced by the on-site spin-orbit interaction lambda(L.S) in a toy model of vanadium chains. In the lambda->0 limit, the decoupled spin and orbital sectors are described by a Haldane and an Ising chain, respectively. The gapped ground state is composed of a ferro-orbital order and a spin liquid with finite correlation lengths. In the opposite limit, strong spin-orbital entanglement results in a simultaneous spin and orbital-moment ordering, which can be viewed as an orbital liquid. Using a combination of analytical arguments and density-matrix renormalization group calculation, we show that an intermediate phase, where the ferro-orbital state is accompanied by a spin Neel order, is bounded on both sides by Ising transition lines. Implications for vanadium compounds CaV2O4 and ZnV2O4 are also discussed.