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Time evolution of the quantum Ising model in two dimensions using Tree Tensor Networks
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abstract
The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the dynamics of the quantum Ising model in two dimensions. Within the perturbative regime of small transverse fields, TTNs faithfully reproduce analytically known, but non-trivial and physically interesting results, for lattices up to $16 \times 16$ sites. Limitations of the method related to the rapid growth of entanglement entropy are explored within more general, paradigmatic quench settings. We provide and discuss comprehensive benchmarks regarding the benefit of \emph{GPU} acceleration and the impact of using local operator sums on the performance.
Forward citations
Cited by 2 Pith papers
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Roughening dynamics of interfaces in the two-dimensional quantum Ising model
In the 2D transverse-field Ising model, domain wall interfaces show long-lived prethermal plateaus in the smooth-interface regime, linked to an interface roughening transition and captured by a 1D solid-on-solid model.
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Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
Classical simulations of the 2D transverse-field Ising model are reliable for quasi-adiabatic annealing across methods, but near-critical post-quench dynamics defeats MPS, TTN, 2DTN-BP, and NQS beyond tJ≈2.
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