Exactly Solvable Counting Statistics in Open Weakly Coupled Interacting Spin Systems

Abstract

We study the full counting statistics for interacting quantum many-body spin systems weakly coupled to the environment. In the leading order in the system-bath coupling, we derive exact spin current statistics for a large class of parity symmetric spin-$1/2$ systems driven by a pair of Markovian baths with local coupling operators. Interestingly, in this class of systems the leading-order current statistics are universal and do not depend on details of the Hamiltonian. Furthermore, in the specific case of a symmetrically boundary driven anisotropic Heisenberg ($XXZ$) spin-$1/2$ chain, we explicitly derive the third-order nonlinear corrections to the current statistics. DOI: http://dx.doi.org/10.1103/PhysRevLett.112.067201 © 2014 American Physical Society