Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain

Fabien Alet (1, 2) , Sylvain Capponi (1, 2) , H. Nonne (3) , P. Lecheminant (3) , I. P. Mcculloch

1 FFC - Fermions Fortement Corrélés (LPT)
2 LPT - Laboratoire de Physique Théorique
3 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation

The zero-temperature properties of the SO(5) bilinear-biquadratic Heisenberg spin chain are investigated by means of a low-energy approach and large scale numerical calculations. In sharp contrast to the spin-1 SO(3) Heisenberg chain, we show that the SO(5) Heisenberg spin chain is dimerized with a two-fold degenerate ground state. On top of this gapful phase, we find the emergence of a non-degenerate gapped phase with hidden (Z$_2$ $\times$ Z$_2$)$^2$ symmetry and spin-3/2 edge states that can be understood from a SO(5) AKLT wave function. We derive a low-energy theory describing the quantum critical point which separates these two gapped phases. It is shown and confirmed numerically that this quantum critical point belongs to the SO(5)$_1$ universality class.

Domaines: Autre [cond-mat.other]

Fabien Alet, Sylvain Capponi, H. Nonne, P. Lecheminant, I. P. Mcculloch. Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2011, 83, pp.060407(R). ⟨10.1103/PhysRevB.83.060407⟩. ⟨hal-00587961⟩