Quantum kinetic perturbation theory for near-integrable spin chains with weak long-range interactions
CITATION: Duval, C. & Kastner, M. 2019. Quantum kinetic perturbation theory for near-integrable spin chains with weak long-range interactions. New Journal of Physics, 21:093021, doi:10.1088/1367-2630/ab3994.
The original publication is available at https://iopscience.iop.org
Publication of this article was funded by the Stellenbosch University Open Access Fund
For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several truncations of the time evolution equations up to eighth order in the Jordan–Wigner fermionic operators. The resulting set of differential equations can be solved for lattices with O(10²) sites and facilitates the computation of spin expectation values and correlation functions to high accuracy, at least for moderate timescales. We use this scheme to study the relaxation dynamics of the model, involving prethermalisation and thermalisation. The techniques developed here can be generalised to other spin models with weak integrability-breaking terms.