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Projected BCS states and spin Hamiltonians for the SO(n)1 Wess-Zumino-Witten model

H. Tu

Published Jan 14, 2013• 0 citations
OpenAlex

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Projected BCS states and spin Hamiltonians for the SO( n ) 1 Wess-Zumino-Witten model

Hong-Hao Tu

We propose a class of projected BCS wave functions and derive their parent spin Hamiltonians. These wave functions can be formulated as infinite matrix product states constructed by chiral correlators of Majorana fermions. In one dimension, the spin Hamiltonians can be viewed as SO($n$) generalizations of Haldane-Shastry models. We numerically compute the spin-spin correlation functions and R\'enyi entropies for $n=5$ and 6. Together with the results for $n=3$ and 4, we conclude that these states are critical and their low-energy effective theory is the SO($n$)${}_{1}$ Wess-Zumino-Witten model. In two dimensions, we show that the projected BCS states are chiral spin liquids, which support non-Abelian anyons for odd $n$ and Abelian anyons for even $n$.

arXiv:1210.1481•Physical Review B•Jan 14, 2013•41 citations

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SO($n$) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU($n$) spin chains

Yueshui Zhang, Ying-Hai Wu, Meng Cheng +1 more

We construct a class of conformal boundary states in the \mathrm{SU}(n)_1 S U ( n ) 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding \mathrm{Spin}(n)_2 \subset \mathrm{SU}(n)_1 S p i n ( n ) 2 ⊂ S U ( n ) 1 . These boundary states are beyond the standard Cardy construction and possess \mathrm{SO}(n) S O ( n ) symmetry. The \mathrm{SU}(n) S U ( n ) Uimin-Lai-Sutherland (ULS) spin chains, which realize the \mathrm{SU}(n)_1 S U ( n ) 1 WZW model on the lattice, allow us to identify these boundary states as the ground states of the \mathrm{SO}(n) S O ( n ) Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the \mathrm{SU}(n) S U ( n ) ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.

arXiv:2508.13114•SciPost Physics•Mar 2, 2026•1 citation
We propose a class of projected BCS wave functions and derive their parent spin Hamiltonians. These wave functions can be formulated as infinite matrix product states constructed by chiral correlators of Majorana fermions. In one dimension, the spin Hamiltonians can be viewed as SO(nnn) generalizations of Haldane-Shastry models. We numerically compute the spin-spin correlation functions and R\'enyi entropies for n=5n=5n=5 and 6. Together with the results for n=3n=3n=3 and 4, we conclude that these states are critical and their low-energy effective theory is the SO(nnn)1{}_{1}1​ Wess-Zumino-Witten model. In two dimensions, we show that the projected BCS states are chiral spin liquids, which support non-Abelian anyons for odd nnn and Abelian anyons for even nnn.
SO(nnn) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(nnn) spin chains
We construct a class of conformal boundary states in the \mathrm{SU}(n)_1 S U ( n ) 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding \mathrm{Spin}(n)_2 \subset \mathrm{SU}(n)_1 S p i n ( n ) 2 ⊂ S U ( n ) 1 . These boundary states are beyond the standard Cardy construction and possess \mathrm{SO}(n) S O ( n ) symmetry. The \mathrm{SU}(n) S U ( n ) Uimin-Lai-Sutherland (ULS) spin chains, which realize the \mathrm{SU}(n)_1 S U ( n ) 1 WZW model on the lattice, allow us to identify these boundary states as the ground states of the \mathrm{SO}(n) S O ( n ) Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the \mathrm{SU}(n) S U ( n ) ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.