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arXiv · 2008.11537

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

Tomohiro Hashizume
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Abstract

Motivated by the experimental realisation of the two-dimensional triangular spin lattice at the National Instate of Standards and Technology in 2012, we developed a new algorithm which allows a time evolution of an MPS with a Hamiltonian with long-range interactions. The algorithm is based on generalised Suzuki-Trotter decompositions with Krylov subspace expansion steps. In the benchmark tests, it predicted the correct local magnetisation behaviour within 5 decimal places up to t\sim 8, it provided the ground state energy of Haldane-Shastry odel correctly up to 4 decimal places for evolution with 64 sites; and it gave a global magnetisation behaviour which agrees with Time Dependent Variational Principle algorithm. The algorithm is applied to a global quench on the triangular Ising lattice on the surface of an infinite cylinder. The algorithm successfully showed the thermalisation of the initial state after a deep quench proving that the algorithm works on time evolutions in a quasi-two-dimensional system.

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Tomohiro Hashizume. 2020-07-01. Numerical Probe of Dynamical Properties of a Two-Dimensional Triangular Ising Lattice with Long-Range Interaction. https://arxiv.org/abs/2008.11537

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