The DiSSEP (Dissipative Symmetric Simple Exclusion Process) was introduced by Crampe et.al. as an integrable one-parameter deformation of the SSEP (Symmetric Simple Exclusion Process). It allows the creation and annihilation of pairs of adjacent particles in addition to the forward and backward hops of the SSEP.

We note that the Markov matrix of the DiSSEP admits a local lattice supersymmetry in the manner of Fendley et.al. and Hagendorf for a particular value of the creation/annihilation rate. The supercharge for this is conjugate to that of the diagonal limit of an XXZ Hamiltonian, consistent with the conjugation relation between an XXZ Hamiltonian and the DiSSEP Markov matrix.

In addition, at an unphysical negative value of the creation/annihilation rate the DiSSEP Markov matrix is conjugate to the XXZ Hamiltonian at its combinatorial point and hence also displays the supersymmetry there.