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.
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.
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.
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.
Abstract The aim of this paper is the investigation of properties of the energy current of usual (frequently found in the literature) boundary driven spin systems. For inhomogeneous Heisenberg (XXZ and XXX) spin chains, we numerically compute the steady state, in the absence of an external magnetic field, and confirm the previously shown occurrence of the one-way street phenomenon, precisely, there is a nonzero energy current that preserves its magnitude and direction as we invert the baths at the edges, an effect stronger than the perfect rectification (which means current in a direction and zero current as we invert the baths). The consideration of several different polarizations at the edges reestablishes that it is a ubiquitous phenomenon. And, even for these inhomogeneous versions of spin chains, we also establish, by analytical methods, other symmetry properties of the energy current and confirm them by numerical computations.
The understanding of non equilibrium quantum systems and, more specifically, of properties of their energy and spin currents has not only a great theoretical interest but also a technological one. In this dissertation, we will clarify the importance of this area by studying certain models that, although simple, already present the occurrence of interesting phenomena. We studied one-dimensional spin chains from the Heisenberg model and XXZ model with a graded structure that are coupled with reservoirs that tend to fix the edge spins in certain directions (target polarization). The rectification of the energy and spin currents and the recent discovered “one-way street” phenomenon [1] were analyzed in view of the conditions necessary for its emergence and maintenance. The latter, which consists in the absence of change of direction of the energy current when the baths are inverted, can initially seems to lead to a violation of the second law of thermodynamics but this is not the case because the energy current consists not only of a contribution due to heat but also one due to work [2–4] this leads us to a parallel with the emergent field of study of quantum thermodynamics that also was discussed briefly. In particular, the use of symmetries of the Lindblad equation was made in the deduction of the existence of those phenomena which allowed that the results found were independent of the transport regime and the size of the chain. Moreover, other interesting phenomena already described in the literature found through this approach were also presented. Finally, as an original result from the author, with a paper published in EPL (Europhysics Letters), the one-way street phenomenon has been extended to more general baths (but still target polarization) with pair of polarization that include directions with arbitrary angles on one side relative to a fixed direction on the other.
This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths at their end points. We take graded versions of the model, i.e. asymmetric chains in which some structure gradually changes in space. We investigate how we can manipulate and control the energy and spin currents of such chains by tuning external and/or inner parameters. In particular, we describe the occurrence of energy current rectification and its reversal due to the application of external magnetic fields. We show that, after carefully chosen inner parameters for the system, by turning on an external magnetic field we can find spin and energy currents propagating in different directions. More interestingly, we may find cases in which rectifications of energy and spin currents occur in opposite directions, i.e. if the energy current is larger when flowing from left to right side, then the spin current is larger if it flows from right to left side. We still describe situations with inversion of the energy current direction as we increase the system asymmetry. We stress that our work aims the development of theoretical knowledge as well as the stimulation of future experimental applications.
We consider accurate investigation of the energy current and its components, heat and work, in some boundary-driven quantum spin systems. The expressions for the currents, as well as the associated Lindblad master equation, are obtained via a repeated interaction scheme. We consider small systems in order to analytically compute the steady distribution to study the current in the steady state. Asymmetrical XXZ and quantum Ising models are detailed analyzed. For the XXZ chain we present cases in which different compositions of heat and work currents, obtained via the repeated interaction protocol, lead to the same energy current, which may be obtained via the Lindblad master equation. For the quantum Ising chain, we describe a case of zero energy current and novanishing heat and work currents. Our findings make clear that to talk about heat in these boundary-driven spin quantum systems we must go beyond an investigation involving only the Lindblad master equation.