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Condens. Matter 2018, 3(4), 32; https://doi.org/10.3390/condmat3040032

Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

Beijing Computational Science Research Center, Beijing 100193, China
Received: 15 September 2018 / Revised: 7 October 2018 / Accepted: 13 October 2018 / Published: 15 October 2018
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Abstract

The Jordan–Wigner transformation plays an important role in spin models. However, the non-locality of the transformation implies that a periodic chain of N spins is not mapped to a periodic or an anti-periodic chain of lattice fermions. Since only the N 1 bond is different, the effect is negligible for large systems, while it is significant for small systems. In this paper, it is interesting to find that a class of periodic spin chains can be exactly mapped to a periodic chain and an anti-periodic chain of lattice fermions without redundancy when the Jordan–Wigner transformation is implemented. For these systems, possible high degeneracy is found to appear in not only the ground state, but also the excitation states. Further, we take the one-dimensional compass model and a new XY-XY model ( σ x σ y σ x σ y ) as examples to demonstrate our proposition. Except for the well-known one-dimensional compass model, we will see that in the XY-XY model, the degeneracy also grows exponentially with the number of sites. View Full-Text
Keywords: periodic spin chains; Jordan–Wigner transformation; degeneracy periodic spin chains; Jordan–Wigner transformation; degeneracy
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Fan, S. Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians. Condens. Matter 2018, 3, 32.

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