Transport in boundary-driven quantum spin systems: One-way street for the energy current

Abstract

We study transport properties in boundary-driven asymmetric quantum spin chains given by $XXZ$ and $XXX$ Heisenberg models. Our approach exploits symmetry transformations in the Lindblad master equation associated to the dynamics of the systems. We describe the mathematical steps to build the unitary transformations related to the symmetry properties. For general target polarizations, we show the occurrence of the one-way street phenomenon for the energy current, namely, the energy current does not change in magnitude and direction as we invert the baths at the boundaries. We also analyze the spin current in some situations, and we prove the uniqueness of the steady state for all investigated cases. Our results, involving nontrivial properties of the energy flow, shall interest researchers working on the control and manipulation of quantum transport.

References in corpus (20)

• Thermal conduction in classical low-dimensional lattices
• Phononics: Manipulating heat flow with electronic analogs and beyond
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Heat Transport in low-dimensional systems
• 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
• 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
• The thermodynamic cost of driving quantum systems by their boundaries
• Exact matrix product solution for the boundary-driven Lindblad $XXZ$-chain
• Towards quantum simulation with circular Rydberg atoms
• Hub Synchronization in Scale-Free Networks
• 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
• 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
• One-way street for the energy current: A ubiquitous phenomenon in boundary-driven quantum spin chains

Cited by in corpus (2)

• Criteria for Davies Irreducibility of Markovian Quantum Dynamics
• Quantum master equation approach to heat transport in dielectrics and semiconductors