Quantifying the accuracy of steady states obtained from the Universal Lindblad Equation

Abstract

We show that steady-state expectation values predicted by the universal Lindblad equation (ULE) are accurate up to bounded corrections that scale linearly with the effective system-bath coupling, $\Gamma$ (second order in the microscopic coupling). We also identify a near-identity, quasilocal "memory-dressing" transformation, used during the derivation of the ULE, whose inverse can be applied to achieve relative deviations of observables that generically scale to zero with $\Gamma$, even for nonequilibrium currents whose steady-state values themselves scale to zero with $\Gamma$. This result provides a solution to recently identified limitations on the accuracy of Lindblad equations, which highlighted a potential for significant relative errors in currents of conserved quantities. The transformation we identify allows for high-fidelity computation of currents in the weak-coupling regime, ensuring thermodynamic consistency and local conservation laws, while retaining the stability and physicality of a Lindblad-form master equation.

5 pages + 2 figures in the main text. 1 figure in the Appendix

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• Semidefinite programming for understanding the limitations of Lindblad equations
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• Error bounds on the universal Lindblad equation in the thermodynamic limit