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.

arXiv comment4 pages, 4 figures

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• Realizing all $so(N{)}_1$ quantum criticalities in symmetry protected cluster models
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
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• Intermediate Haldane phase in spin-2 quantum chains with uniaxial anisotropy
• Symmetry-protected topological order and negative-sign problem for SO(N) bilinear-biquadratic chains
• Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
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• Nickel-Titanium double perovskite: A three-dimensional spin-1 Heisenberg antiferromagnet
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• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Symmetry-protected topological order identified via Gutzwiller-guided density-matrix-renormalization-group: $\mathrm{SO}(n)$ spin chains
• Impurity screening by defects in (1+1)$d$ quantum critical systems
• SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains