Exactly solvable counting statistics in weakly coupled open 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 symmetrically boundary driven anisotropic Heisenberg ($XXZ$) spin 1/2 chain we derive explicitly the third-order non-linear corrections to the current statistics.

4 pages in RevTex, with 1 pdf figure, version as accepted by Phys. Rev. Lett

References in corpus (14)

• An Open-System Quantum Simulator with Trapped Ions
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• PT-symmetric quantum Liouvillian dynamics
• Counting statistics of coherent population trapping in quantum dots
• Detection of non-Gaussian Fluctuations in a Quantum Point Contact
• Exact large-deviation statistics for a nonequilibrium quantum spin chain
• Quantum transport in quantum networks and photosynthetic complexes at the steady state
• Scattering Approach to Counting Statistics in Quantum Pumps
• Full counting statistics of Luttinger liquid conductor

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