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Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks | | Sheng-Hsuan Lin
; Michael Zaletel
; Frank Pollmann
; | | Date: |
15 Dec 2021 | | Abstract: | We investigate the computational power of the recently introduced class of
isometric tensor network states (isoTNSs), which generalizes the isometric
conditions of the canonical form of one-dimensional matrix-product states to
tensor networks in higher dimensions. We discuss several technical details
regarding the implementation of isoTNSs-based algorithms and compare different
disentanglers -- which are essential for an efficient handling of isoTNSs. We
then revisit the time evolving block decimation for isoTNSs ($ ext{TEBD}^2$)
and explore its power for real time evolution of two-dimensional (2D) lattice
systems. Moreover, we introduce a density matrix renormalization group
algorithm for isoTNSs ($ ext{DMRG}^2$) that allows to variationally find
ground states of 2D lattice systems. As a demonstration and benchmark, we
compute the dynamical spin structure factor of 2D quantum spin systems for two
paradigmatic models: First, we compare our results for the transverse field
Ising model on a square lattice with the prediction of the spin-wave theory.
Second, we consider the Kitaev model on the honeycomb lattice and compare it to
the result from the exact solution. | | Source: | arXiv, 2112.08394 | | Services: | Forum | Review | PDF | Favorites | |
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