Exact steady state of the open XX-spin chain: entanglement and transport properties
arXiv:2102.10036 · doi:10.1103/PRXQuantum.2.030344
Abstract
We study the reduced dynamics of open quantum spin chains of arbitrary length with nearest neighbour interactions, immersed within an external constant magnetic field along the direction, whose end spins are weakly coupled to heat baths at different temperatures, via energy preserving couplings. We find the analytic expression of the unique stationary state of the master equation obtained in the so-called global approach based on the spectralization of the full chain Hamiltonian. Hinging upon the explicit stationary state, we reveal the presence of sink and source terms in the spin-flow continuity equation and compare their behaviour with that of the stationary heat flow. Moreover, we also obtain analytic expressions for the steady state two-spin reduced density matrices and for their concurrence. We then set up an algorithm suited to compute the stationary bipartite entanglement along the chain and to study its dependence on the Hamiltonian parameters and on the bath temperatures.
References in corpus (73)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Entanglement of a Pair of Quantum Bits
- Thermal conduction in classical low-dimensional lattices
- An Open-System Quantum Simulator with Trapped Ions
- Open Quantum Systems. An Introduction
- Fundamental aspects of steady-state conversion of heat to work at the nanoscale
- Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport
- Spin transport in a one-dimensional anisotropic Heisenberg model
- A thermoelectric heat engine with ultracold atoms
- Exact nonequilibrium steady state of a strongly driven open XXZ chain
- On the Local and Global Approaches to Quantum Transport and Violation of the Second-law of Thermodynamics
- Markovian master equations for quantum thermal machines: local vs global approach
- Markovian Master Equations: A Critical Study
- Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance
- Reconciliation of quantum local master equations with thermodynamics
- The Josephson heat interferometer
- Modeling heat transport through completely positive maps
- Non-equilibrium steady-states in a driven-dissipative superfluid
- Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
- Testing the validity of the local and global GKLS master equations on an exactly solvable model
- Performance bound for quantum absorption refrigerators
- Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
- Open Quantum Dynamics: Complete Positivity and Entanglement
- Exact matrix product solution for the boundary-driven Lindblad -chain
- Perturbative treatment of inter-site couplings in the local description of open quantum networks
- Matrix product solutions of boundary driven quantum chains
- Autonomous quantum thermal machine for generating steady-state entanglement
- Controlling and measuring quantum transport of heat in trapped-ion crystals
- Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions
- Non-additive dissipation in open quantum networks out of equilibrium
- Thermal Conductance of a Single-Electron Transistor
- Symmetry and the thermodynamics of currents in open quantum systems
- Heat transport in the spin chain: from ballistic to diffusive regimes and dephasing enhancement
- Current in open quantum systems
- Diffusive high-temperature transport in the one-dimensional Hubbard model
- Transport in open spin chains: A Monte Carlo wave-function approach
- High-temperature coherent transport in the XXZ chain in the presence of an impurity
- Quantum Markovian master equations: resonance theory shows validity for all time scales
- Adding dynamical generators in quantum master equations
- Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains
- Thermodynamic consistency of the optomechanical master equation
- Thermodynamic deficiencies of some simple Lindblad operators
- Heat flux operator, current conservation and the formal Fourier's law
- Non-equilibrium quantum chains under multi-site Lindblad baths
- Two coupled qubits interacting with a thermal bath: A comparative study of different models
- Topological Heat Transport and Symmetry-Protected Boson Currents
- Critical heat current for operating an entanglement engine
- Thermal transport in out of equilibrium quantum harmonic chains
- 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
- Microscopic theory of a non-equilibrium open bosonic chain
- Heat, Work and Energy Currents in the Boundary-Driven XXZ Spin Chain
- Quantum transport in d-dimensional lattices
- The open Heisenberg chain under boundary fields: a magnonic logic gate
- Current fluctuations in boundary-driven quantum spin chains
- Master equation for dissipative interacting qubits in a common environment
- Alternation of sign of magnetization current in driven XXZ chains with twisted XY boundary gradients
- Interplay of different environments in open quantum systems: Breakdown of the additive approximation
- Quantum current in dissipative systems
- Energy transport between two pure-dephasing reservoirs
- Heat transport in quantum spin chains: the relevance of integrability
- Going beyond Local and Global approaches for localized thermal dissipation
- Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current
- Bath assisted transport in a three-site spin chain: global {\sl vs} local approach
- Controlling heat and particle currents in nanodevices by quantum observation
- Nonreciprocal Quantum Transport at Junctions of Structured Leads
- Scale-invariant freezing of entanglement
- Equilibration and nonclassicality of a double-well potential
- Determinant representations of spin-operator matrix elements in the XX spin chain and their applications
- Anomalous currents in driven XXZ chain with boundary twisting at weak coupling or weak driving
- Excitation injector in an atomic chain: long-ranged transport and efficiency amplification
- Full decoherence induced by local fields in open spin chains with strong boundary couplings