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

References in corpus (5)

• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states
• Competing orders in the generalized Hund chain model at half-filling
• Continuous quantum phase transition between two topologically distinct valence bond solid states associated with the same spin value

Cited by in corpus (3)

• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• All spin-1 topological phases in a single spin-2 chain
• Nickel-Titanium double perovskite: A three-dimensional spin-1 Heisenberg antiferromagnet