Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Spin transport in a Lindblad-driven isotropic quantum Heisenberg spin-chain

Leon Droenner, Nicolas L. Naumann, Markus Heyl, Alexander Carmele

Published Feb 22, 2017• 0 citations
Publisher

Abstract

We investigate the spin transport properties of an isotropic quantum Heisenberg spin-chain. Driving the system out of equilibrium via two different reservoirs at the boundaries, the system exhibits negative differential conductivity for strong driving. We describe the system-reservoir interaction with a Lindblad approach. We show that the interplay between Lindblad dynamics and system dynamics influences highly the spin current. For weak driving, equal rates maximize the current while strong driving shows a counter intuitive behavior. Our findings could guide to an understanding of the transport properties which are dependent on the external driving.

DOI
10.1117/12.2252076

Related papers

Boundary-driven Heisenberg chain in the long-range interacting regime: Robustness against far-from-equilibrium effects

Leon Droenner, Alexander Carmele

We investigate the Heisenberg $XXZ$ chain with long-range interactions in the $Z$ dimension. By applying two magnetic boundary reservoirs, we drive the system out of equilibrium and induce a nonzero steady-state current. The long-range coupled chain shows nearly ballistic transport and linear response for all potential differences of the external reservoirs. In contrast, the common isotropic nearest-neighbor coupling shows negative differential conductivity and a transition from diffusive to subdiffusive transport for a far-from-equilibrium driving. Adding disorder, the change in the transport for nearest-neighbor coupling is therefore highly dependent on the driving. We find for the disordered long-range coupled $XXZ$ chain, any change in the transport behavior is independent of the potential difference and the coupling strengths of the external reservoirs.

arXiv:1706.07744•Physical review. B./Physical review. B•Nov 16, 2017•11 citations

Behavior of magnetic currents in anisotropic Heisenberg spin chains out of equilibrium

Vladislav Popkov, Mario Salerno, Gunter Markus Schutz

The behavior of the magnetic currents in one-dimensional Heisenberg XXZ spin chains kept out of equilibrium by boundary driving fields is investigated. In particular, the dependence of the spin currents on the anisotropy parameter Δ and on the boundary fields is studied both analytically and numerically in the framework of the Lindblad master equation formalism. We show that the spin current can be maximized with appropriate choices of the boundary fields, and for odd system sizes, N, we demonstrate the existence of additional symmetries that cause the current to be an odd function of Δ. From direct numerical integrations of the quantum master equation, we find that for an arbitrary N the current J(z)(N) vanishes for Δ=0, while for Δ negative it alternates its sign with the system size. In the gapless critical region |Δ|<1, the scaling of the current is shown to be J(z)(N)∼1/N while in the gapped region |Δ|>1 we find that J(z)(N)∼exp(-αN). A simple mean-field approach, which predicts rather well the values of J(z)(N) for the gapped region and the values of the absolute current maxima in the critical region, is developed. The existence of two different stationary solutions for the mean-field density matrix in the whole parameter range is also demonstrated.

Physical Review E•Mar 22, 2012•17 citations

A nonequilibrium quantum phase transition in strongly coupled spin chains

Eduardo Mascarenhas, Giacomo Giudice, Vincenzo Savona

We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport phases.

arXiv:1703.02934•Quantum•Dec 20, 2017•11 citations

Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium

Giuliano Benenti, Giulio Casati, Tomaž Prosen +2 more

We study the charge conductivity in one-dimensional prototype models of interacting particles, such as the Hubbard and the $t\text{\ensuremath{-}}V$ spinless fermion models, when coupled to some external baths injecting and extracting particles at the boundaries. We show that, if these systems are driven far from equilibrium, a negative differential conductivity regime can arise. The above electronic models can be mapped into Heisenberg-like spin ladders coupled to two magnetic baths, so that charge transport mechanisms are explained in terms of quantum spin transport. The negative differential conductivity is due to oppositely polarized ferromagnetic domains that arise at the edges of the chain and therefore inhibit spin transport: we propose a qualitative understanding of the phenomenon by analyzing the localization of one-magnon excitations created at the borders of a ferromagnetic region. We also show that negative differential conductivity is stable against breaking of integrability. Numerical simulations of nonequilibrium time evolution have been performed by employing a Monte Carlo wave function approach and a matrix product operator formalism.

arXiv:0901.2032•Physical Review B•Jul 8, 2009•120 citations

Boundary-driven Lindblad dynamics of random quantum spin chains: strong disorder approach for the relaxation, the steady state and the current

Cécile Monthus

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.

arXiv:1701.02102•Journal of Statistical Mechanics Theory and Experiment•Apr 1, 2017•20 citations

Negative differential conductivity in far-from-equilibrium quantum spin chains

Giuliano Benenti, Giulio Casati, Tomaž Prosen +1 more

We show that, when a finite anisotropic Heisenberg spin-1/2 chain in the gapped regime is driven far from equilibrium, oppositely polarized ferromagnetic domains build up at the edges of the chain, thus suppressing quantum spin transport. As a consequence, a negative differential conductivity regime arises, where increasing the driving decreases the current. The above results are explained in terms of magnon localization and are shown to be structurally stable against breaking of integrability.

arXiv:0806.2236•Europhysics Letters (EPL)•Feb 1, 2009•75 citations
We investigate the spin transport properties of an isotropic quantum Heisenberg spin-chain. Driving the system out of equilibrium via two different reservoirs at the boundaries, the system exhibits negative differential conductivity for strong driving. We describe the system-reservoir interaction with a Lindblad approach. We show that the interplay between Lindblad dynamics and system dynamics influences highly the spin current. For weak driving, equal rates maximize the current while strong driving shows a counter intuitive behavior. Our findings could guide to an understanding of the transport properties which are dependent on the external driving.
We investigate the Heisenberg XXZXXZXXZ chain with long-range interactions in the ZZZ dimension. By applying two magnetic boundary reservoirs, we drive the system out of equilibrium and induce a nonzero steady-state current. The long-range coupled chain shows nearly ballistic transport and linear response for all potential differences of the external reservoirs. In contrast, the common isotropic nearest-neighbor coupling shows negative differential conductivity and a transition from diffusive to subdiffusive transport for a far-from-equilibrium driving. Adding disorder, the change in the transport for nearest-neighbor coupling is therefore highly dependent on the driving. We find for the disordered long-range coupled XXZXXZXXZ chain, any change in the transport behavior is independent of the potential difference and the coupling strengths of the external reservoirs.
The behavior of the magnetic currents in one-dimensional Heisenberg XXZ spin chains kept out of equilibrium by boundary driving fields is investigated. In particular, the dependence of the spin currents on the anisotropy parameter Δ and on the boundary fields is studied both analytically and numerically in the framework of the Lindblad master equation formalism. We show that the spin current can be maximized with appropriate choices of the boundary fields, and for odd system sizes, N, we demonstrate the existence of additional symmetries that cause the current to be an odd function of Δ. From direct numerical integrations of the quantum master equation, we find that for an arbitrary N the current J(z)(N) vanishes for Δ=0, while for Δ negative it alternates its sign with the system size. In the gapless critical region |Δ|<1, the scaling of the current is shown to be J(z)(N)∼1/N while in the gapped region |Δ|>1 we find that J(z)(N)∼exp(-αN). A simple mean-field approach, which predicts rather well the values of J(z)(N) for the gapped region and the values of the absolute current maxima in the critical region, is developed. The existence of two different stationary solutions for the mean-field density matrix in the whole parameter range is also demonstrated.
We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport phases.
We study the charge conductivity in one-dimensional prototype models of interacting particles, such as the Hubbard and the $t\text{\ensuremath{-}}V$ spinless fermion models, when coupled to some external baths injecting and extracting particles at the boundaries. We show that, if these systems are driven far from equilibrium, a negative differential conductivity regime can arise. The above electronic models can be mapped into Heisenberg-like spin ladders coupled to two magnetic baths, so that charge transport mechanisms are explained in terms of quantum spin transport. The negative differential conductivity is due to oppositely polarized ferromagnetic domains that arise at the edges of the chain and therefore inhibit spin transport: we propose a qualitative understanding of the phenomenon by analyzing the localization of one-magnon excitations created at the borders of a ferromagnetic region. We also show that negative differential conductivity is stable against breaking of integrability. Numerical simulations of nonequilibrium time evolution have been performed by employing a Monte Carlo wave function approach and a matrix product operator formalism.
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.