Effective field theory for the SO(n) bilinear-biquadratic spin chain

Abstract

We present a low-energy effective field theory to describe the SO(n) bilinear-biquadratic spin chain. We start with n=6 and construct the effective theory by using six Majorana fermions. After determining various correlation functions we characterize the phases and establish the relation between the effective theories for SO(6) and SO(5). Together with the known results for n=3 and 4, a reduction mechanism is proposed to understand the ground state for arbitrary SO(n). Also, we provide a generalization of the Lieb-Schultz-Mattis theorem for SO(n). The implications of our results for entanglement and correlation functions are discussed.

5 pages, 1 figure, published version

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• Gutzwiller Approach for Elementary Excitations in $S=1$ Antiferromagnetic Chains
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
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• Symmetry-protected topological order identified via Gutzwiller-guided density-matrix-renormalization-group: $\mathrm{SO}(n)$ spin chains
• The c-d conjecture
• SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains
• Impurity screening by defects in (1+1)$d$ quantum critical systems
• Universality of Short Distance Corrections to Quantum Optics