Tensor network simulation of chains of non-Markovian open quantum systems

Fux, Gerald E.; Kilda, Dainius; Lovett, Brendon W.; Keeling, Jonathan

doi:10.48550/arxiv.2201.05529

Cited by 3 publications

(3 citation statements)

References 66 publications

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“…This is particularly aided by the fact that local Lindblad equations are favourable for tensor network techniques. Studying such dynamics at finite temperatures is often quite challenging otherwise, requiring simulation of non-Markovian dynamics [56][57][58].…”

Section: Discussionmentioning

confidence: 99%

Searching for Lindbladians obeying local conservation laws and showing thermalization

Tupkary¹,

Dhar²,

Kulkarni³

et al. 2023

Preprint

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We investigate the possibility of a Markovian quantum master equation (QME) that consistently describes a finite-dimensional system, a part of which is weakly coupled to a thermal bath. In order to preserve complete positivity and trace, such a QME must be of Lindblad form. For physical consistency, it should additionally preserve local conservation laws and be able to show thermalization. First, we show that the microscopically derived Redfield equation (RE) violates complete positivity unless in extremely special cases. We then prove that imposing complete positivity and demanding preservation of local conservation laws enforces the Lindblad operators and the lamb-shift Hamiltonian to be 'local', i.e, to be supported only on the part of the system directly coupled to the bath. We then cast the problem of finding 'local' Lindblad QME which can show thermalization into a semidefinite program (SDP). We call this the thermalization optimization problem (TOP). For given system parameters and temperature, the solution of the TOP conclusively shows whether the desired type of QME is possible up to a given precision. Whenever possible, it also outputs a form for such a QME. For a XXZ chain of few qubits, fixing a reasonably high precision, we find that such a QME is impossible over a considerably wide parameter regime when only the first qubit is coupled to the bath. Remarkably, we find that when the first two qubits are attached to the bath, such a QME becomes possible over much of the same paramater regime, including a wide range of temperatures.

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Section: Discussionmentioning

confidence: 99%

Searching for Lindbladians obeying local conservation laws and showing thermalization

Tupkary¹,

Dhar²,

Kulkarni³

et al. 2023

Preprint

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“…Recent advances have extended the applicability of numerically exact process tensor techniques to many-body systems [63] and multiple environments [64]. Those techniques could be combined with the moment generating functional method we have described here to expose the dynamics of environments in such situations.…”

Section: Discussionmentioning

confidence: 99%

Using the Environment to Understand non-Markovian Open Quantum Systems

Gribben

Strathearn

Fux

et al. 2022

Quantum

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Tracing out the environmental degrees of freedom is a necessary procedure when simulating open quantum systems. While being an essential step in deriving a tractable master equation it represents a loss of information. In situations where there is strong interplay between the system and environmental degrees of freedom this loss makes understanding the dynamics challenging. These dynamics, when viewed in isolation, have no time-local description: they are non-Markovian and memory effects induce complex features that are difficult to interpret. To address this problem, we here show how to use system correlations, calculated by any method, to infer any correlation function of a Gaussian environment, so long as the coupling between system and environment is linear. This not only allows reconstruction of the full dynamics of both system and environment, but also opens avenues into studying the effect of a system on its environment. In order to obtain accurate bath dynamics, we exploit a numerically exact approach to simulating the system dynamics, which is based on the construction and contraction of a tensor network that represents the process tensor of this open quantum system. Using this we are able to find any system correlation function exactly. To demonstrate the applicability of our method we show how heat moves between different modes of a bosonic bath when coupled to a two-level system that is subject to an off-resonant drive.

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“…While we have focused on well-justified weak coupling approaches for simulating quantum dynamics in this work, it is worth noting that studies involving more rigorous simulation methods -such as numerically exact tensor network approaches [61][62][63] (which have recently been applied to chainlike systems [64]) or other non-Markovian techniques [65] may lead to further interesting insights into the interplay between coherent and dissipative dynamics within these quantum transport systems.…”

Section: Discussionmentioning

confidence: 99%

Eliminating radiative losses in long-range exciton transport

Davidson,

Pollock,

Gauger

2022

Preprint

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We demonstrate that it is possible to effectively eliminate radiative losses during excitonic energy transport in systems with an intrinsic energy gradient. By considering chain-like systems of repeating 'unit' cells which can each consist of multiple sites, we show that tuning a single system parameter (the intra-unit-cell coupling) leads to efficient and highly robust transport over relatively long distances. This remarkable transport performance is shown to originate from a partitioning of the system's eigenstates into energetically-separated bright and dark subspaces, allowing long range transport to proceed efficiently through a 'dark chain' of eigenstates. Finally, we discuss the effects of intrinsic dipole moments, which are of particular relevance to molecular architectures, and demonstrate that appropriately-aligned dipoles can lead to additional protection against other (non-radiative) loss processes. Our dimensionless open quantum systems model is designed to be broadly applicable to a range of experimental platforms.

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Tensor network simulation of chains of non-Markovian open quantum systems

Cited by 3 publications

References 66 publications

Searching for Lindbladians obeying local conservation laws and showing thermalization

Searching for Lindbladians obeying local conservation laws and showing thermalization

Using the Environment to Understand non-Markovian Open Quantum Systems

Eliminating radiative losses in long-range exciton transport

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