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

Abstract

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.

4 pages, 4 figures

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• String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states
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