A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
Open Access
- 1 July 2012
- journal article
- research article
- Published by IOP Publishing in New Journal of Physics
- Vol. 14 (7), 073007
- https://doi.org/10.1088/1367-2630/14/7/073007
Abstract
We study quantum transport properties of an open Heisenberg XXZ spin 1/2 chain driven by a pair of Lindblad jump operators satisfying a global 'micro-canonical' constraint, i.e. conserving the total magnetization. We will show that this system has an additional discrete symmetry that is specific to the Liouvillean description of the problem. Such symmetry reduces the dynamics even more than would be expected in the standard Hilbert space formalism and establishes existence of multiple steady states. Interestingly, numerical simulations of the XXZ model suggest that a pair of distinct non-equilibrium steady states becomes indistinguishable in the thermodynamic limit, and exhibit sub-diffusive spin transport in the easy-axis regime of anisotropy Δ > 1.Keywords
Other Versions
This publication has 36 references indexed in Scilit:
- Colloquium: Nonequilibrium dynamics of closed interacting quantum systemsReviews of Modern Physics, 2011
- Many-body physics with ultracold gasesReviews of Modern Physics, 2008
- Third quantization: a general method to solve master equations for quadratic open Fermi systemsNew Journal of Physics, 2008
- Modeling heat transport through completely positive mapsPhysical Review E, 2007
- Normal-transport behavior in finite one-dimensional chaotic quantum systemsEurophysics Letters, 2006
- Fourier's law in a quantum spin chain and the onset of quantum chaosEurophysics Letters, 2005
- Fourier's Law confirmed for a class of small quantum systemsZeitschrift für Physik B Condensed Matter, 2003
- Strong evidence of normal heat conduction in a one-dimensional quantum systemEurophysics Letters, 2003
- On the generators of quantum dynamical semigroupsCommunications in Mathematical Physics, 1976
- Completely positive dynamical semigroups of N-level systemsJournal of Mathematical Physics, 1976