Tensor Network Approach for Efficient Ground State Preparation and Dynamical Simulations in 2D systems

In this work, we develop a variational technique based on 2D tensor networks for efficient ground state preparation of the honeycomb Kitaev model. Our approach utilizes the centralizer ansatz, ensuring both accuracy and computational efficiency in state preparation. First, we demonstrate high-fidelity preparation of the Kitaev spin liquid ground state in the absence of an external field by exploiting the model's inherent symmetries. We then extend our study to non-zero magnetic fields, thus breaking the symmetry constraints, and show that our algorithm remains effective for sufficiently large system sizes. Finally, we apply our tensor network-based method to investigate the dynamics in honeycomb lattice and other lattice geometries, laying the groundwork for the development of quantum digital twins for specific Hamiltonians.