Validating Phase-Space Methods with Tensor Networks in Two-Dimensional Spin Models with Power-Law Interactions.

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Quantum Simulation

Background:

• Accurate simulation of quantum dynamics is crucial for understanding complex many-body systems.
• Two-dimensional (2D) quantum models, particularly XXZ models, are relevant for quantum technologies.
• Tensor network methods and semiclassical approximations offer different approaches to simulating quantum dynamics.

Purpose of the Study:

• To evaluate the dynamics of 2D power-law interacting XXZ models using a time-dependent variational principle for matrix product states.
• To compare the accuracy and efficiency of semiclassical phase-space calculations (discrete truncated Wigner approximation - DTWA) against tensor network methods.
• To validate predictions for generating scalable entangled resources for quantum metrology.

Main Methods:

• Employed an extension of the time-dependent variational principle for matrix product states to model 2D XXZ model dynamics.
• Calculated spin squeezing as a measure of quantum correlations.
• Utilized the discrete truncated Wigner approximation (DTWA) for semiclassical phase-space calculations and compared with tensor network results.

Main Results:

• DTWA efficiently and accurately captures the scaling of entanglement with system size in 2D XXZ models.
• DTWA steady-state behavior aligns with tensor network thermal ensemble calculations.
• The study provides a benchmark for dynamical calculations in 2D quantum systems.

Conclusions:

• Semiclassical DTWA is a reliable and efficient method for simulating entanglement dynamics in 2D quantum systems.
• This work rigorously validates methods for generating scalable entangled resources for quantum metrology.
• The findings facilitate benchmarking and validation of quantum dynamical simulations.