One-way street for the energy current: A ubiquitous phenomenon in boundary-driven quantum spin chains

Abstract

Focusing on the description of nontrivial properties of the energy transport at quantum scale, we investigate asymmetrical quantum spin chains described by boundary-driven $XXZ$ and $XXX$ 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 independent 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.

References in corpus (23)

• Phononics: Manipulating heat flow with electronic analogs and beyond
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Thermal diode: Rectification of heat flux
• An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays
• Controlling the energy flow in nonlinear lattices: a model for a thermal rectifier
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Asymmetric Properties of Heat Conduction in a One-Dimensional Frenkel-Kontorova Model
• On the Local and Global Approaches to Quantum Transport and Violation of the Second-law of Thermodynamics
• Reconciliation of quantum local master equations with thermodynamics
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• The thermodynamic cost of driving quantum systems by their boundaries
• Exact matrix product solution for the boundary-driven Lindblad $XXZ$-chain
• Graded anharmonic crystals as genuine thermal diodes: Analytical description of rectification and negative differential thermal resistance
• Sufficient conditions for thermal rectification in graded materials
• Driven isotropic Heisenberg spin chain with arbitrary boundary twisting angle: exact results
• Thermal Rectification in Graded Materials
• Energy Rectification in Quantum Graded Spin Chains: Analysis of the XXZ Model
• Manipulating energy and spin currents in nonequilibrium systems of interacting qubits
• Comments on boundary driven open XXZ chain: asymmetric driving and uniqueness of steady states
• Heat, Work and Energy Currents in the Boundary-Driven XXZ Spin Chain
• The open Heisenberg chain under boundary fields: a magnonic logic gate
• Rectification and One-Way Street for the Energy Current in Boundary-Driven Asymmetric Quantum Spin Chains

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• Beyond the Lindblad Master Equation: Heat, Work and Energy Currents in Boundary Driven Spin Chains
• Rectification induced by geometry in two-dimensional quantum spin lattices
• Transport in boundary-driven quantum spin systems: One-way street for the energy current