A study of dissipative models based on Dirac matrices

• URL: http://arxiv.org/abs/2308.05245v2
• Date: Fri, 8 Sep 2023 00:05:57 GMT
• Title: A study of dissipative models based on Dirac matrices
• Authors: Jyotsna Gidugu and Daniel P. Arovas
• Abstract summary: We generalize the recent work of Shibata and Katsura, who considered a S=1/2 chain with alternating XX and YY couplings in the presence of dephasing. Our generalization involves Dirac gamma matrix spin' operators on the square lattice, and maps onto a non-Hermitian square lattice bilayer which is also Kitaev-solvable. We use a genetic algorithm to estimate the Liouvillian gap and the first decay modes for large system sizes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We generalize the recent work of Shibata and Katsura, who considered a S=1/2 chain with alternating XX and YY couplings in the presence of dephasing, the dynamics of which are described by the GKLS master equation. Their model is equivalent to a non-Hermitian system described by the Kitaev formulation in terms of a single Majorana species hopping on a two-leg ladder in the presence of a nondynamical Z_2 gauge field. Our generalization involves Dirac gamma matrix `spin' operators on the square lattice, and maps onto a non-Hermitian square lattice bilayer which is also Kitaev-solvable. We describe the exponentially many non-equilibrium steady states in this model. We identify how the spin degrees of freedom can be accounted for in the 2d model in terms of the gauge-invariant quantities and then proceed to study the Liouvillian spectrum. We use a genetic algorithm to estimate the Liouvillian gap and the first decay modes for large system sizes. We observe a transition in the first decay modes, similar to that found by Shibata and Katsura. The results we obtain are consistent with a perturbative analysis for small and large values of the dissipation strength.

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