CMT Forum: Dan Arovas

I will discuss a generalization of the Shibata-Katsura model (2019) of a dissipative quantum spin chain to a two dimensional system where the Pauli spin operators are extended to 4x4 Dirac matrices.  The evolution of the system’s reduced density matrix is governed by the GKLS master equation, which can be expressed as non-Hermitian Hamiltonian evolution in a doubled Hilbert space.  As with the SK model, the particular form of the Hamiltonian and Lindblad jump operators result in the system being “solvable” in the sense of Kitaev’s honeycomb lattice model.  I.e., the resulting Hamiltonian corresponds to (non-Hermitian) hopping of noninteracting Majorana fermions in the presence of a Z2 gauge field.  The model has a large number of nonequilibrium steady states (NESS), each of which corresponds to infinite temperature.  We numerically find the asymptotic relaxation rate to the NESS block.