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Physics Letters A

Energy transport in boundary driven quantum spin systems: One-way street phenomenon in models with long range interactions

Emmanuel Pereira, Humberto C. F. Lemos

Published Sep 4, 2020• 1 citation
Publisher
DOI
10.1016/j.physleta.2020.126864

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Motivated by the demand for efficient quantum devices to engineer energy transport, we analyze some inhomogeneous quantum spin systems, including XXZ chains, with magnetization baths at the ends. With a goal of finding general properties, we study the effects of suitable transformations on the boundary-driven Lindblad master equation associated with the dynamics of the systems. For asymmetric models with target polarization at the edges or twisted XY boundary gradients, we show the properties of the steady state, which establish the features of the energy current irrespective of the system size and the regime of transport. We show the ubiquitous occurrence of energy rectification and, more interestingly, of an unusual phenomenon: in the absence of an external magnetic field, there is a one-way street for the energy current, i.e., the direction of the energy current does not change as we invert the magnetization baths at the boundaries. Given the extensiveness of the procedures, which essentially involve the properties of the Lindblad master equation, our results certainly follow for other interactions and other boundary conditions. Moreover, our results indicate graded spin chains as genuine quantum rectifiers.

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Focusing on the description of nontrivial properties of the energy transport at quantum scale, we investigate asymmetrical quantum spin chains described by boundary-driven and Heisenberg models. We search for symmetries properties of the Lindblad master equation related to the dynamics of the system in order to establish properties of the steady state. Under rather general assumptions for the target polarization at the boundaries, we show the occurrence of an effect related to (but stronger than) energy rectification, namely, the one-way street phenomenon, which is the existence of an unique way for the energy flow. Precisely, the energy current does not change in magnitude and direction as we invert the baths at the boundaries: its direction is completely determined by the asymmetry in the bulk of the chain. The results follow independently of the system size and of the transport regime. Our findings show the ubiquitous occurrence of the one-way street phenomenon for the energy flow in boundary-driven spin systems and, we believe, they shall be an useful contribution to the area devoted to the investigation and building of efficient quantum devices used to control and manipulate the energy current.
Abstract We study transport properties in boundary-driven asymmetric quantum spin chains given by XXZ and XXX Heisenberg models. Our approach exploits symmetry transformations in the Lindblad master equation associated to the dynamics of the systems. We describe the mathematical steps to build the unitary transformations related to the symmetry properties. For general target polarizations, we show the occurrence of the one-way street phenomenon for the energy current, namely, the energy current does not change in magnitude and direction as we invert the baths at the boundaries. We also analyze the spin current in some situations, and we prove the uniqueness of the steady state for all investigated cases. Our results, involving nontrivial properties of the energy flow, shall interest researchers working on the control and manipulation of quantum transport.
Motivated by the demand for efficient quantum devices to engineer energy transport, we analyze some inhomogeneous quantum spin systems, including XXZ chains, with magnetization baths at the ends. With a goal of finding general properties, we study the effects of suitable transformations on the boundary-driven Lindblad master equation associated with the dynamics of the systems. For asymmetric models with target polarization at the edges or twisted XY boundary gradients, we show the properties of the steady state, which establish the features of the energy current irrespective of the system size and the regime of transport. We show the ubiquitous occurrence of energy rectification and, more interestingly, of an unusual phenomenon: in the absence of an external magnetic field, there is a one-way street for the energy current, i.e., the direction of the energy current does not change as we invert the magnetization baths at the boundaries. Given the extensiveness of the procedures, which essentially involve the properties of the Lindblad master equation, our results certainly follow for other interactions and other boundary conditions. Moreover, our results indicate graded spin chains as genuine quantum rectifiers.