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arXiv:1007.3472 · Physical Review B

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

Gia-Wei Chern, Natalia Borisovna Perkins, G. I. Japaridze

Published Nov 18, 2010• 6 citations
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Abstract

We study quantum phase transitions induced by the on-site spin-orbit interaction $\ensuremath{\lambda}\mathbf{L}\ensuremath{\cdot}\mathbf{S}$ in a toy model of vanadium chains. In the $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ 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 N\'eel order, is bounded on both sides by Ising transition lines. Implications for vanadium compounds ${\text{CaV}}_{2}{\text{O}}_{4}$ and ${\text{ZnV}}_{2}{\text{O}}_{4}$ are also discussed.

DOI
10.1103/physrevb.82.172408

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