We construct a dual symmetry-protected topological Hamiltonian for the U(1) symmetric anisotropic spin-$\frac{1}{2}$ Heisenberg chain, a model that has traditionally been used to study spontaneous symmetry breaking in both ferromagnetic and antiferromagnetic phases, with an intervening extended Luttinger liquid phase. By performing a nonlocal 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 nonlocal string order parameter and constructing an exact zero-mode operator that connects states in different fermionic parity sectors.

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• Symmetry protected topological states
• Topological phases of matter
• Heisenberg model
• Luttinger liquid model
• Spin chains