What is the topological dual of the XXZ spin Chain?

2025/07/29 by Tang, Yicheng, Kattel, Pradip, Andrei, Natan
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2507.22119

Abstract

We construct a dual symmetry-protected topological (SPT) Hamiltonian for the U(1) symmetric anisotropic spin-(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.

Citations

• Edge modes and boundary impurities in the anisotropic Heisenberg spin chain
• Edge Spin fractionalization in one-dimensional spin-S quantum antiferromagnets
• Spin fractionalization and zero modes in the spin-(1)/(2) XXZ chain with boundary fields

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