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EN
Several non-singular 2-component methods for relativistic calculations of the electronic structure of atoms and molecules lead to cumbersome operators which are partly defined in the coordinate representation and partly in the momentum representation. The replacement of the Fourier transform technique by the approximate resolution of identity in the basis set of approximate eigenvectors of the p^{2} operator is investigated in terms of the possible inaccuracies involved in this method. The dependence of the accuracy of the evaluated matrix elements on the composition of the subspace of these eigenvectors is studied. Although the method by itself appears to be quite demanding with respect to the faithfulness of the representation of the p^{2} operator, its performance in the context of the standard Gaussian basis sets is found to be encouragingly accurate. This feature is interpreted in terms of approximately even-tempered structure of the majority of Gaussian basis sets used in atomic and molecular calculations.
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EN
In the framework of the matrix product states representation the effect of the single-ion anisotropy on the time evolution of the initial state after a sudden quench of the local magnetic field has been investigated. The overlap of the initial and time-evolved states, so called the Loschmidt echo, magnetization profiles and correlation functions are presented.
EN
In the framework of the matrix product state representation the effect of a sudden turning on of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated. Depending on the value of the uniaxial anisotropy parameter, the calculations were derived within (or outside) the region where the Haldane gap survives. An exact expression for the time evolution of the Loschmidt echo has been derived and, moreover, its collapse and revival behaviour was captured. In addition, the non-local order parameter of a time evolving state was tracked, revealing two types of relaxations.
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