Abstract A model consisting of two quantum XX spin chains, one homogeneous and the second with random couplings drawn from a binary distribution, is considered. The two chains are coupled to two different non-local thermal baths and their dynamics is governed by a Lindblad equation. In the steady state, a current J is induced between the two chains by coupling them together by their edges and imposing different chemical potentials μ to the two baths. While a regime of linear characteristics J versus Δ μ is observed in the absence of randomness, a gap opens as the disorder strength is increased. In the infinite-randomness limit, this behavior is related to the density of states of the localized states contributing to the current. The conductance is shown to diverge in this limit.
Abstract The Lindblad dynamics of the XX quantum chain with large random fields h j (the couplings J j can be either uniform or random) is considered for boundary-magnetization-drivings acting on the two end-spins. Since each boundary-reservoir tends to impose its own magnetization, we first study the relaxation spectrum in the presence of a single reservoir as a function of the system size via some boundary-strong-disorder renormalization approach. The non-equilibrium-steady-state in the presence of two reservoirs can be then analyzed from the effective renormalized Linbladians associated to the two reservoirs. The magnetization is found to follow a step profile, as found previously in other localized chains. The strong disorder approach allows to compute explicitly the location of the step of the magnetization profile and the corresponding magnetization-current for each disordered sample in terms of the random fields and couplings.
Abstract The Lindblad dynamics with dephasing in the bulk and magnetization-driving at the two boundaries is studied for the quantum spin chain with random fields h j and couplings J j (that can be either uniform or random). In the regime of strong disorder in the random fields, or in the regime of strong bulk-dephasing, the effective dynamics can be mapped onto a classical simple symmetric exclusion process with quenched disorder in the diffusion coefficient associated to each bond. The properties of the corresponding non-equilibrium-steady-state in each disordered sample between the two reservoirs are studied in detail by extending the methods that have been previously developed for the symmetric exclusion process without disorder. Explicit results are given for the magnetization profile, for the two-point correlations, for the mean current and for the current fluctuations, in terms of the random fields and couplings defining the disordered sample.
We will review some known exact solutions for the steady state of the open quantum Heisenberg
XXZ spin chain coupled to a pair of baths [Phys. Rev. Lett. 107, 137201 (2011).]. The dynamics is modelled by the Lindblad master equation. We also review how to calculate some relevant physical observables and provide the statistics of spin current assuming the spin chain is weakly coupled to the baths [Phys. Rev. Lett. 112, 067201 (2014).].
We study an open quantum spin chain of arbitrary length with nearest neighbor
XX interactions of strength
g, immersed in an external constant magnetic field $\mathrm{\ensuremath{\Delta}}$ along the
z direction, whose end spins are weakly coupled to two heat baths at different temperatures. In the so-called global approach, namely, without neglecting interspin interactions, using standard weak-coupling limit techniques, we first derive the open chain master equation written in terms of fermionic mode operators. Then, we focus on the study of the dependence of the resulting open dynamics from the ratio $r\ensuremath{\equiv}g/\mathrm{\ensuremath{\Delta}}$. By increasing
r, some of the chain Bohr transition frequencies become negative; when this occurs, both the generator of the dissipative time evolution and its stationary states behave discontinuously. As a consequence, the asymptotic spin and heat flows also exhibit discontinuities, but in a different way: while source terms in the spin flow continuity equation show jumps, the heat flow instead is continuous but with discontinuous first derivatives with respect to
r. These two behaviors might be experimentally accessible; in particular, they could discriminate between the global and the local approaches to open quantum spin chains. Indeed, the latter one, which neglects interspin interactions in the derivation of the master equation, does not show any kind of discontinuous behavior.
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.
We study the spin transport properties of some disordered spin chains with a special focus on the distribution of the frequency-dependent spin conductivity. In the cases of interest here, the systems are governed by an effectively infinite disorder at low energies. A hallmark of this behavior is the wide discrepancy between the average and the typical values of some physical quantities, which are described by extremely broad distributions. We show that such is also the case of the spin conductivity, whose average value is metallic but whose typical one, the physically relevant quantity, is insulating. This solves the apparent contradiction between the prediction of a spin metallic phase of the spin-1/2 disordered XX chain and its known localized behavior (after a mapping to free fermions). Our results are based on analytical and numerical implementations of a strong-disorder renormalization group as well as exact diagonalization studies. We present our analyses in very general terms, valid for systems of any spin
S value, but the cases of
S=1/2 and 1 are studied in greater detail.