Vmc with PEPS Advances 2D System Ground State Calculations

Key Takeaways

• Autoregressive row updates replace local Metropolis moves.
• Autocorrelation times drop dramatically near critical points.
• Ground‑state energies lower for 2D Ising and spin glass.
• Computational cost comparable to traditional local sampling.
• Optimization stability improves in frustrated quantum systems.

Pulse Analysis

Accurately solving the many‑body ground‑state problem has long been a bottleneck in computational physics, especially for two‑dimensional tensor‑network states like PEPS. Conventional PEPS‑VMC algorithms rely on local spin‑flip proposals, which become inefficient near criticality due to diverging autocorrelation times. By embedding an autoregressive, single‑layer row‑wise contraction scheme, the new method generates non‑local configuration proposals that preserve the favorable scaling of PEPS while dramatically improving sampling efficiency.

The row‑wise update strategy was rigorously tested on the transverse‑field Ising model and a quantum spin glass, two archetypal systems that stress conventional samplers. Results reveal a pronounced reduction in autocorrelation, translating into faster convergence toward the true ground state. Moreover, the algorithm consistently achieved lower variational energies and displayed enhanced optimization stability, even in the rugged energy landscape of frustrated spin glasses. Importantly, these gains come without a significant increase in computational overhead, keeping the method accessible for existing high‑performance computing pipelines.

Beyond immediate performance gains, this development opens new avenues for quantum materials research. More reliable PEPS‑VMC simulations can accelerate the exploration of exotic phases in correlated electron systems, such as high‑temperature superconductors modeled by the doped 2D Hubbard Hamiltonian. Future extensions may incorporate explicit conservation constraints or adapt the row‑update paradigm to real‑time evolution and isometric PEPS frameworks, further broadening its applicability. As tensor‑network methods continue to mature, autoregressive row‑wise sampling stands out as a versatile tool that bridges accuracy and scalability.