Validating phase-space methods with tensor networks in two-dimensional spin models with power-law interactions

Abstract

Using a recently developed extension of the time-dependent variational principle for matrix product states, we evaluate the dynamics of 2D power-law interacting XXZ models, implementable in a variety of state-of-the-art experimental platforms. We compute the spin squeezing as a measure of correlations in the system, and compare to semiclassical phase-space calculations utilizing the discrete truncated Wigner approximation (DTWA). We find the latter efficiently and accurately captures the scaling of entanglement with system size in these systems, despite the comparatively resource-intensive tensor network representation of the dynamics. We also compare the steady-state behavior of DTWA to thermal ensemble calculations with tensor networks. Our results open a way to benchmark dynamical calculations for two-dimensional quantum systems, and allow us to rigorously validate recent predictions for the generation of scalable entangled resources for metrology in these systems.

6+4 pages, 3+1 figures

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Cited by in corpus (7)

• Quantum-enhanced sensing on an optical transition via emergent collective quantum correlations
• Two-mode Squeezing in Floquet Engineered Power-law Interacting Spin Models
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Cluster truncated Wigner approximation for bond-disordered Heisenberg spin models
• Two-dimensional correlation propagation dynamics with a cluster discrete phase-space method
• Nonequilibrium Critical Scaling of a Squeezing Phase Transition
• Spin amplification in realistic systems