Open spin chains with dynamic lattice supersymmetry

Abstract

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

arXiv comment33 pages, 2 figures

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• 1D Majorana Goldstinos and partial supersymmetry breaking in quantum wires
• Lattice Supersymmetry in the Open XXZ Model: An Algebraic Bethe Ansatz Analysis
• On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions
• On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions
• Bipartite fidelity of critical dense polymers
• Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes
• On the logarithmic bipartite fidelity of the open XXZ spin chain at $\Delta =-1/2$
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations
• Lattice SUSY for the DiSSEP at ${\lambda }^2=1$ (and ${\lambda }^2=-3$)