The renormalization group flows of the one-dimensional anisotropic XY model and quantum Ising model under a transverse field are obtained by different multiscale entanglement renormalization ansatz schemes. It is shown that the optimized disentangler
removes the short-range entanglement by rotating the system in the parameter space spanned by the anisotropy and the magnetic field. It is understood from the study that the disentangler reduces the entanglement by mapping the system to another one in the same universality class but with smaller short range entanglement. The phase boundary and corresponding critical exponents are calculated using different schemes with different block sizes, look-ahead steps and truncation dimensions. It is shown that larger truncation dimension leads to more accurate results and that using larger block size or look-ahead step improve the overall calculation consistency.
In this paper we study the low temperature kinetics of the electrons in the system composed of a quantum dot connected to two leads by solving the equation of motion. The decoherence and the relaxation of the system caused by the gate voltage noise a
nd electron-phonon scattering are investigated. In order to take account of the strong correlation of the electrons in this system, the quasi-exact wave functions are calculated using an improved matrix product states algorithm. This algorithm enables us to calculate the wave functions of the ground state and the low lying excited states with satisfied accuracy and thus enables us to study the kinetics of the system more effectively. It is found that although both of these two mechanisms are proportional to the electron number operator in the dot, the kinetics are quite different. The noise induced decoherence is much more effective than the energy relaxation, while the energy relaxation and decoherence time are of the same order for the electron-phonon scattering. Moreover, the noise induced decoherence increases with the lowering of the dot level, but the relaxation and decoherence due to the electron-phonon scattering decrease.
This paper has been withdrawn by the author and replaced by arXiv:0809.4751
