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arXiv:2112.12824 · Physical review. B./Physical review. B

Exact weak bosonic zero modes in a spin/fermion chain

Jianlong Fu

Published Oct 28, 2022• 5 citations
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Abstract

We study an exactly solvable one-dimensional spin-$\frac{1}{2}$ model which can support weak zero modes in its ground-state manifold. The spin chain has staggered $XXZ$-type and $ZZ$-type spin interaction on neighboring bonds and is thus dubbed the ($XXZ,Z$) chain. The model is equivalent to an interacting fermionic chain by Jordan-Wigner transformation. We study the phase diagram of the system and work out the conditions and properties of its weak zero modes. In the fermion chain representation, these weak zero modes are given by even-order polynomials of Majorana fermion operators and are thus bosonic. The fermionic chain Hamiltonian contains only fermion hopping and interaction terms and may have potential realization in experiments.

DOI
10.1103/physrevb.106.l161412

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A Spin 1/21/21/2 Fermions Chain with XYXYXY Interaction
We consider a chain of spinful fermions with nearest neighbor hopping in the presence of a XYXYXY antiferromagnetic interaction. The XYXYXY term is mapped onto a Kitaev chain at half-filling such that displays a bosonic zero mode topologically protected and long-range order. As the strength of the hopping amplitude is changed, the system undergoes a quantum phase transition from the topological non-trivial to the trivial phase. We apply the finite-size scaling method to determinate the phase diagram of the model.
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