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.
Fendley, Strong zero modes and eigenstate phase tran- sitions in the xyz/interacting majorana chain, Journal of Physics A: Mathematical and Theoretical 49, 30LT01 (2016)
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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.