Open spin chains with dynamic lattice supersymmetry
(2017) Journal of Physics A: Mathematical and Theoretical — Vol. 50, p. 185202 (2017)
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- Abstract
- The quantum spin 1/2 XXZ chain with anisotropy parameter Δ=−1/2 possesses a dynamic supersymmetry on the lattice. This supersymmetry and a generalisation to higher spin are investigated in the case of open spin chains. A family of non-diagonal boundary interactions that are compatible with the lattice supersymmetry and depend on several parameters is constructed. The cohomology of the corresponding supercharges is explicitly computed as a function of the parameters and the length of the chain. For certain specific values of the parameters, this cohomology is shown to be non-trivial. This implies that the spin-chain ground states are supersymmetry singlets. Special scalar products involving an arbitrary number of these supersymmetry singlets for chains of different lengths are exactly computed. As a physical application, the logarithmic bipartite fidelity of the open quantum spin 1/2 XXZ chain with Δ=−1/2 and special diagonal boundary interactions is determined.
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Walmsley Hagendorf, C., & Liénardy, J. (2017). Open spin chains with dynamic lattice supersymmetry. Journal of Physics A: Mathematical and Theoretical, 50, 185202. https://doi.org/10.1088/1751-8121/aa67ff (Original work published 2017)