Efficient energy resolved quantum master equation for transport calculations in large strongly correlated systems

Abstract

We introduce a systematic approximation for an efficient evaluation of Born–Markov master equations for steady state transport studies in open quantum systems out of equilibrium: the energy resolved master equation approach. The master equation is formulated in the eigenbasis of the open quantum system and build successively by including eigenstates with increasing grandcanonical energies. In order to quantify convergence of the approximate scheme we introduce quality factors to check preservation of trace, positivity and hermiticity. Furthermore, we discuss different types of master equations that go beyond the commonly used secular approximation in order to resolve coherences between quasi-degenerate states. For the discussion of complete positivity we introduce a canonical Redfield–Bloch master equation and compare it to a previously derived master equations in Lindblad form with and without using the secular approximation. The approximate scheme is benchmarked for a six orbital quantum system which shows destructive quantum interference under the application of a bias voltage. The energy resolved master equation approach presented here makes quantum transport calculations in many-body quantum systems numerically accessible also beyond six orbitals with a full Hilbert space of the order of ∼106.

Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems

“…, independently of the details of the interaction. Note that previous works have highlighted the appearance of steady-state coherences in the presence of (quasi)degeneracies [67][68][69], while here coherences are completely washed out; this fact is known to be rooted in the full secular approximation that we assumed.…”

“…Existing investigations of LGKS master equations for quadratic many-body systems typically rely on a local system-environment approach [25,33,[60][61][62][63][64]. The possibility of having a nonlocal equation has been considered much more rarely [65,66] and a rigorous microscopic derivation has been performed only for specific systems [67][68][69][70][71]. A related class of quadratic bosonic system has been also studied exactly, i.e., without even making the Born-Markov approximation [72].…”

All-electric electron spin resonance studied by means of Floquet quantum master equations

“…We proceed similarly to Refs. [32,[43][44][45][46][47][48] to derive the quantum master equation by treating the coupling between the impurity and the reservoirs at the lowest (second) order in perturbation theory in H T (equivalent to the Born-Markov approximation [35,55]) in the framework of nonequilibrium Green's function formalism. This is appropriate for the 245435-3 description of the sequential tunneling regime, which corresponds to the effective tunneling between the two reservoirs dominated by processes where the electrons hop from one of the reservoirs to the system and then to the other reservoir.…”

Topological signatures in a weakly dissipative Kitaev chain of finite length

“…Relaxing the above condition may lead to memory effects that give rise to more complex situations governed by integro-differential master equations, whose description poses some subtleties which are still the object of research. Even restricting ourselves to Markovian master equations, a proper description of interactions with the environment generally requires full knowledge of the eigendecomposition of the system Hamiltonian, which is feasible only for special classes of many-body systems or in specific situations [4][5][6][7][8][9]. In fact, most studies in the many-body realm stick with local forms of Lindblad jump operators in the master equations (see, e.g., Ref.…”