The U(1)-symmetric XXZ spin chain is dual, via a modified Jordan-Wigner transformation, to a local fermionic model whose two gapped phases are topological and which are separated by a critical Luttinger liquid.
Oshikawa, Hidden z2* z2 symmetry in quantum spin chains with arbitrary integer spin, Journal of Physics: Condensed Matter 4, 7469 (1992)
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What is the topological dual of the XXZ spin Chain?
The U(1)-symmetric XXZ spin chain is dual, via a modified Jordan-Wigner transformation, to a local fermionic model whose two gapped phases are topological and which are separated by a critical Luttinger liquid.