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Spin fractionalization and zero modes in the spin-$\frac{1}{2}$ XXZ chain with boundary fields
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abstract
In this work we argue that the antiferromagnetic spin $\frac{1}{2}$ XXZ chain in the gapped phase with boundary magnetic fields hosts fractional spin $\frac{1}{4}$ at its edges. Using a combination of Bethe ansatz and the density matrix renormalization group we show that these fractional spins are sharp quantum observables in both the ground and the first excited state as the associated fractional spin operators have zero variance. In the limit of zero edge fields, we argue that these fractional spin operators once projected onto the low energy subspace spanned by the ground state and the first excited state, identify with the strong zero energy mode discovered by P. Fendley \cite{Fendley}.
Forward citations
Cited by 3 Pith papers
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Complete Boundary Phase Diagram of the Spin-$\frac{1}{2}$ XXZ Chain with Boundary Fields in the Anti-Ferromagnetic Gapped Regime
The complete boundary field phase diagram of the gapped XXZ chain is derived, with phases classified by ground state and by the number of boundary bound states, which equals the number of spectral towers.
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Emergent boundary supersymmetry in a one dimensional superconductor
A one-dimensional superconductor with two boundary magnetic impurities has a special 'supersymmetric' point where the nine degenerate low-energy boundary states form spl(2,1)⊗spl(2,1) representations and support zero ...
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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.
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