What is the topological dual of the XXZ spin Chain?
Abstract
We construct a dual symmetry-protected topological (SPT) Hamiltonian for the U(1) symmetric anisotropic spin-12 Heisenberg chain-a model that has traditionally been used to study spontaneous symmetry breaking (SSB) in both ferromagnetic and antiferromagnetic phases, with an intervening extended Luttinger liquid phase. By performing a non-local unitary transformation, we explicitly construct a local fermionic Hamiltonian that exhibits two nontrivial topological phases separated by an extended Luttinger liquid regime. We demonstrate the topological nature of these phases by analyzing the entanglement structure, deriving a non-local string order parameter, and constructing an exact zero mode operator that connects states in different fermionic parity sectors.
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