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arXiv · 1612.02951

Open spin chains with dynamic lattice supersymmetry

Christian Hagendorf·Jean Liénardy
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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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Christian Hagendorf, Jean Liénardy. 2016-12-09. Open spin chains with dynamic lattice supersymmetry. https://doi.org/10.1088/1751-8121%2Faa67ff

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