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.
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.
In order to better understand the minimal ingredients for thermal rectification, we perform a detailed investigation of a simple spin chain, namely, the open XX model with a Lindblad dynamics involving global dissipators. We use a Jordan-Wigner transformation to derive a mathematical formalism to compute the heat currents and other properties of the steady state. We have rigorous results to prove the occurrence of thermal rectification even for slightly asymmetrical chains. Interestingly, we describe cases where the rectification does not decay to zero as we increase the system size, that is, the rectification remains finite in the thermodynamic limit. We also describe some numerical results for more asymmetrical chains. The presence of thermal rectification in this simple model indicates that the phenomenon is of general occurrence in quantum spin systems.
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.
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.
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.
In this work we study the heat transport in an XXZ spin-1/2 Heisenberg chain with homogeneous magnetic field, incoherently driven out of equilibrium by reservoirs at the boundaries. We focus on the effect of bulk dephasing (energy-dissipative) processes in different parameter regimes of the system. The non-equilibrium steady state of the chain is obtained by simulating its evolution under the corresponding Lindblad master equation, using the time evolving block decimation method. In the absence of dephasing, the heat transport is ballistic for weak interactions, while being diffusive in the strongly-interacting regime, as evidenced by the heat-current scaling with the system size. When bulk dephasing takes place in the system, diffusive transport is induced in the weakly-interacting regime, with the heat current monotonically decreasing with the dephasing rate. In contrast, in the strongly-interacting regime, the heat current can be significantly enhanced by dephasing for systems of small size.
We study a recently discussed XX spin chain with nonlocal dephasing [Y.-P. Wang et al., arXiv:2310.03069] in a steady-state boundary-driven setting, confirming superdiffusive magnetization transport in the thermodynamic limit. The emergence of superdiffusion is rather interesting as the Lindblad operators causing it are a coherent sum of two terms, each of which would separately cause diffusion. One therefore has a quantum phenomenon where a coherent sum of two diffusive terms results in superdiffusion. We also study perturbations of the superdiffusive model, finding that breaking the exact form of dissipators, as well as adding interactions to the XX chain, results in superdiffusion changing into diffusion.