Open spin chains with dynamic lattice supersymmetry

The quantum spin $1\mathrm{/}2$ XXZ chain with anisotropy parameter $\mathrm{\Delta }=-1\mathrm{/}2$ 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 $1\mathrm{/}2$ XXZ chain with $\mathrm{\Delta }=-1\mathrm{/}2$ and special diagonal boundary interactions is determined.