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Motivated by the experimental realisation of the two-dimensional triangularspin lattice at the National Instate of Standards and Technology in 2012, wedeveloped a new algorithm which allows a time evolution of an MPS with aHamiltonian with long-range interactions. The algorithm is based on generalisedSuzuki-Trotter decompositions with Krylov subspace expansion steps. In thebenchmark tests, it predicted the correct local magnetisation behaviour within5 decimal places up to t\sim 8, it provided the ground state energy ofHaldane-Shastry odel correctly up to 4 decimal places for evolution with 64sites; and it gave a global magnetisation behaviour which agrees with TimeDependent Variational Principle algorithm. The algorithm is applied to a globalquench on the triangular Ising lattice on the surface of an infinite cylinder.The algorithm successfully showed the thermalisation of the initial state aftera deep quench proving that the algorithm works on time evolutions in aquasi-two-dimensional system.

Numerical Probe of Dynamical Properties of a Two-Dimensional Triangular Ising Lattice with Long-Range Interaction