Multiple quantum NMR spin dynamics in one-dimensional quantum spin chains

Multiple quantum NMR dynamics of spin-12 carrying molecules of a gas in nanopores

“…Although the first phenomenological approach was developed together with the experimental realization of MQ NMR [1] the consistent quantum-mechanical theory is not developed up to now except for one-dimensional systems. In particular, the one-dimensional spin chain with nearest neighbor double quantum Hamiltonian [1] is exactly solvable and it has been shown that, starting with a thermodynamic equilibrium state, only zero and double quantum coherences are produced [8]- [10]. This conclusion has been confirmed experimentally for relatively small excitation times [11,12].…”

“…However, next-nearest couplings and other distant interactions lead to higher order coherences in MQ NMR spectra. These interactions are beyond the exact solvable models [8]- [10]. Thus one should apply numerical methods in order to take into account distant spin-spin couplings.…”

Implementation of State Transfer Hamiltonians in Spin Chains with Magnetic Resonance Techniques

“…Modelling the physical spin system by an ensemble of equivalent and independent spin chains with nearest-neighbour couplings only, we can derive analytical formulas for the evolution to fit the experimental data. Under this approximation, the DQ Hamiltonian is exactly solvable by invoking a Jordan-Wigner mapping onto a system of free fermions [149,162]. The analytical solution for the evolution of the thermal state, when measuring the collective magnetization, is given by [119,134]:…”

Solid-state multiple quantum NMR in quantum information processing: exactly solvable models

“…Efforts to understand these experimental results were limited to arguments involving less than typically 10 spins. An exact solution for MQ NMR spin dynamics in an infinite one-dimensional quantum spin chain with NN dipolar interactions has been obtained in the high-temperature approximation [46] as well as in the low-temperature case [47]. This model is the first exactly solvable model in MQ NMR for a system with a macroscopic number of coupled spins.…”

“…Our motivations and justifications include the following: (i) the hope to gain insights, understanding and predictions of some features of MQ NMR in materials with quasi-one-dimensional distributions of spins [40,44,45], (ii) in many cases, consideration of only NN dipolar interactions in a one-dimensional chain is a reasonable approximation because 83 per cent of the average of the distribution of the dipolar coupling constants in a onedimensional chain is determined by NN interactions [49], (iii) the results can serve as a basis for elaborating a perturbation theory in order to take into account the interactions with remote spins [41] and also extrapolations to higher dimensions, and (iv) the results provide an opportunity to test the validity of other approximation methods in MQ NMR such as the commutator series expansion for the equations of motion of the spin density operator [46]. Numerical [9,50,51] and theoretical [46,52] investigations of onedimensional spin chains have also been performed. Simplified and tractable one-dimensional models [48] yield physical insights into the complexities of many-body spin dynamics [46,52].…”