Hello everyone myself Sudipto. Currently I'm learning the matrix product state technique in order to simulate 1d spin system and study different properties of the system form quantum information theoretic perspective. After reading some nicely written reviews I managed to write a code of to find out the ground state using the MPS formalism, for Ising model. There I use the imaginary time evolution method, in order to get the ground state of the system. However this requires Suzuki Trotter decomposition of the propagator and in my case I am using translational invariant matrix product operator representation of the propagator rather than the even-odd decomposition (see page 42-43 http://arxiv.org/pdf/0907.2796v1.pdf). Unfortunately I got stuck at some conceptual point. My wish us to use extend the code for XY and XYZ model. But in that case what would be the exact trotter decomposition and what would be the form of X*i and C*i matrices that I'm struggling to find out. I've worked out the respective forms for XY (https://docs.google.com/document/d/1l_EzaW7qL6vRRmONnhHqGWqYDfnQvD-QyiyqH2YrB7E/edit?usp=sharing) but could not able to cross check those. So my request is to kindly go through the draft and let me know your opinion so that I can extend the code developed for Ising model , for XY as well as for XYZ.