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arXiv · 2507.22119

What is the topological dual of the XXZ spin Chain?

Yicheng Tang·Pradip Kattel·Natan Andrei
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Abstract

We construct a dual symmetry-protected topological (SPT) 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 (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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Yicheng Tang, Pradip Kattel, Natan Andrei. 2025-07-29. What is the topological dual of the XXZ spin Chain?. https://arxiv.org/abs/2507.22119

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