We addressed the issue of energy and magnetization rectification in the quantum one-dimensional open XXZ spin chain driven out of equilibrium by magnetization pumping applied at its boundaries and in the presence of an external magnetic field. We analyzed the effects of the introduction of an inner graded structure in the chain, as well as the effects of a graded magnetic field in the system. We present theoretical results for the fluxes and also exact solutions, obtained by means of numerical computation, for a small chain. We verified that the energy flux exhibits rectification in both the inner graded structure case and the graded magnetic field one, although the magnetization flux exhibits rectification only in the latter situation. With a view to showing that the rectification is not a phenomenon limited to the studied model, we additionally investigated, by means of computational analysis, distinct configurations of the spin chain regarding the chain size, the internal interactions, and the boundary conditions. We found that the same conditions apply to the existence of rectification, except for one situation: with regard to the twisted XY boundary gradients model, the magnetization flux exhibits rectification for a uniform magnetic field as well.
We addressed the issue of energy and magnetization rectification in the quantum one-dimensional open XXZ spin chain driven out of equilibrium by magnetization pumping applied at its boundaries and in the presence of an external magnetic field. We analyzed the effects of the introduction of an inner graded structure in the chain, as well as the effects of a graded magnetic field in the system. We present theoretical results for the fluxes and also exact solutions, obtained by means of numerical computation, for a small chain. We verified that the energy flux exhibits rectification in both the inner graded structure case and the graded magnetic field one, although the magnetization flux exhibits rectification only in the latter situation. With a view to showing that the rectification is not a phenomenon limited to the studied model, we additionally investigated, by means of computational analysis, distinct configurations of the spin chain regarding the chain size, the internal interactions, and the boundary conditions. We found that the same conditions apply to the existence of rectification, except for one situation: with regard to the twisted XY boundary gradients model, the magnetization flux exhibits rectification for a uniform magnetic field as well.
In this work, with focus on the energy-transport properties in quantum, low-dimensional, graded materials, we address the investigation of the energy (and spin) current in XXZ open chains with graded inner structures and driven out of equilibrium by magnetization pumping applied at the ends. We study several types of graded structures in different situations in order to show a ubiquitous occurrence of energy rectification, even for the system under a homogeneous magnetic field. Due to technical difficulties, we carry out the computation for small chains, but we present arguments that indicate the extension of some results to larger systems. Recalling the generic existence of energy rectification in classical, graded materials, which are described by anharmonic chains of oscillators, and recalling also the anharmonicity of these XXZ models, which involve quartic terms in more transparent representation in terms of fermionic creation and annihilation operators, we may say that our results extend the ubiquity of energy rectification occurrence in classical graded materials to the case of quantum systems.
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.
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.
The focus of this thesis is to investigate non equilibrium properties of a spin 1/2 chain considered as a closed or an open quantum system. In the first case, the non equilibrium situation is generated by means of a quench (sudden change of the hamiltonian); in the second case, we connect unbalanced magnetic reservoirs at the chain edges. In this thesis, we present two works in the context of closed systems and another one in the case of open systems. To describe the dynamics we use the time-dependent extension of Density MatrixRenormalization Group (DMRG) technique. In the first work, we investigate the non equilibrium dynamics generated by a local quenchin a spin system described by the XXZ Heisenberg model. More specifically, the quench involves connecting two chains, one that is prepared in the ferromagnetic phase and another that is in the paramagnetic phase. After the quench, we observe effective light cones inthe maps of the on-site magnetization and the entanglement entropy as a function of site and time, when these quantities are calculated in the chain that had no magnetic order.We show that these light cones are associated with two kinds of excitation characteristic of the XXZ model, more specifically spinons and bound states. Furthermore, we see that, for long times, the system approaches the equilibrium state of the connected chains. systemwill go to the equilibrium state at infinity time.In the second work, we analyze shielding properties that appear in the transverse Ising model. If the site i=L of the chain has null field and the global state is a Gibbs state, the reduced state of the chain in the right side of the i=L site is shown to have no dependence on the parameters of the left chain. We refer to this effect as a shielding property. Wealso study the chain dynamics after a local quench that changes the magnetic field in the first site. We observe a light cone in the on-site magnetization, however the magnetization pulse is reflected by the site with null field.Finally, in the third work, we connect two magnetic reservoirs at the ends of the XXZ Heisenberg spin chain and calculate the spin and energy currents in the non equilibrium steady state (NESS). We investigate if it is possible to control and manipulate such currents and their respective rectifications by the application of an external magnetic field. Forthat, we introduce a graded asymmetry (gradual change of the parameters) in the field and in the anisotropy parameter of the model. For appropriate choice of the field, we observe that it is possible to force the energy and the spin currents to propagate in opposite directions. This means that we invert not only the currents but also their rectificationsthrough external mechanisms.
Thermal rectification is the phenomenon by which the flux of heat depends on the direction of the flow. It has attracted much interest in recent years due to the possibility of devising thermal diodes. In this paper, we consider the rectification phenomenon in the quantum XXZ chain subject to an inhomogeneous field. The chain is driven out of equilibrium by the contact at its boundaries with two different reservoirs, leading to a constant flow of magnetization from one bath to the other. The nonunitary dynamics of this system, which is modeled by a Lindblad master equation, is treated exactly for small sizes and numerically for larger ones. The functional dependence of the rectification coefficient on the model parameters (anisotropy, field amplitude, and out of equilibrium driving strength) is investigated in full detail. Close to the XX point and at small inhomogeneity and low driving, we have found an explicit expression for the rectification coefficient that is valid at all system sizes. In particular, it shows that the phenomenon of rectification persists even in the thermodynamic limit. Finally, we prove that in the case of the XX chain, there is no rectification.
In order to reveal mechanisms to control and manipulate spin currents, we perform a detailed investigation of the dephasing effects in the open XX model with a Lindblad dynamics involving global dissipators and thermal baths. Specifically, we consider dephasing noise modeled by current-preserving Lindblad dissipators acting on graded versions of these spin systems, that is, systems in which the magnetic field and/or the spin interaction are growing (decreasing) along the chain. In our analysis, we study the nonequilibrium steady state via the covariance matrix using the Jordan-Wigner approach to compute the spin currents. We find that the interplay between dephasing and graded systems gives rise to a nontrivial behavior: When we have homogeneous magnetic field and graded interactions we have rectification enhancement mechanisms, and when we have fully graded systems we can control the spin current in order to keep the direction of the particle and/or spin flow even with inverted baths. We describe our result in detailed numerical analysis and we see that rectification in this simple model indicates that the phenomenon may generally occur in quantum spin systems.