Solution of the Lindblad equation for spin helix states

Abstract

Using Lindblad dynamics we study quantum spin systems with dissipative boundary dynamics that generate a stationary nonequilibrium state with a non-vanishing spin current that is locally conserved except at the boundaries. We demonstrate that with suitably chosen boundary target states one can solve the many-body Lindblad equation exactly in any dimension. As solution we obtain pure states at any finite value of the dissipation strength and any system size. They are characterized by a helical stationary magnetization profile and a superdiffusive ballistic current of order one, independent of system size even when the quantum spin system is not integrable. These results are derived in explicit form for the one-dimensional spin-1/2 Heisenberg chain and its higher-spin generalizations (which include for spin-1 the integrable Zamolodchikov-Fateev model and the bi-quadratic Heisenberg chain). The extension of the results to higher dimensions is straightforward.

23 pages, 2 figures

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• Lindblad master equation approach to the topological phase transition in the disordered Su-Schrieffer-Heeger model
• A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model
• Heat, Work and Energy Currents in the Boundary-Driven XXZ Spin Chain
• Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
• The fate of high winding number topological phases in the disordered extended Su-Schrieffer-Heeger model
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Winding up quantum spin helices: How avoided level crossings exile classical topological protection
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space
• Criteria for Davies Irreducibility of Markovian Quantum Dynamics
• Exact solutions of few-magnon problems in the spin-$S$ periodic XXZ chain
• Spin-helix states in the $XXZ$ spin chain with strong dissipation
• Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Quantum spin helices more stable than the ground state: onset of helical protection
• Duality between open systems and closed bilayer systems: Thermofield double states as quantum many-body scars
• Boundary driven $XYZ$ chain: Exact inhomogeneous triangular matrix product ansatz
• Universality in relaxation of spin helices under the $XXZ$- spin chain dynamics
• Invariant subspaces and explicit Bethe vectors in the integrable open spin $1/2$ $\XYZ$ chain
• Exact density profile in a tight-binding chain with dephasing noise
• Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Stable dynamic helix state in the nonintegrable XXZ Heisenberg model
• Transition between dissipatively stabilized helical states
• Dissipative cooling towards phantom Bethe states in boundary driven XXZ spin chain