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

TL;DR

This paper introduces a new algorithm for simulating the time evolution of long-range interacting 2D triangular Ising lattices, demonstrating accurate results and thermalisation behavior in quasi-two-dimensional systems.

Contribution

A novel algorithm based on Suzuki-Trotter and Krylov methods for efficient time evolution of long-range 2D spin systems is developed and validated.

Findings

Accurately predicts local magnetisation up to t~8

Correctly computes ground state energy for 64 sites

Shows thermalisation after deep quench in a 2D lattice

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.