Vmc with PEPS Advances 2D System Ground State Calculations

Scientists are continually striving to accurately model the behaviour of complex quantum systems, and a new study details a significant advance in tackling the many-body ground state problem. Tao Chen, Jing Liu, Yantao Wu, Pan Zhang, and Youjin Deng , from institutions including the Hefei National Laboratory and the University of Science and Technology of China , present a novel Variational Monte Carlo (VMC) method incorporating row-update Projected Entangled-Pair States (PEPS). Their research addresses the limitations of conventional PEPS-VMC algorithms, which often struggle with slow convergence in challenging systems like quantum spin glasses, by introducing an efficient autoregressive row-wise sampling technique. This innovative approach not only accelerates calculations near critical points but also enhances optimisation stability and achieves lower ground-state energies in notoriously difficult spin glass landscapes, potentially paving the way for more powerful quantum simulations.

PEPS-VMC Sampling via Autoregressive Row-wise Contractions offers improved

Scientists have achieved a significant breakthrough in solving the many-body ground state problem, a central challenge in computational physics. This innovative approach addresses limitations in standard PEPS-VMC algorithms, which often suffer from slow convergence and critical slowing down, especially near phase transitions or in systems with complex energy landscapes. The team’s work establishes a robust improvement to local PEPS-VMC sampling, potentially paving the way for more advanced sampling schemes in the future.
The study reveals a method that utilizes autoregressive single-layer row updates to generate collective, non-local configuration proposals, markedly reducing Temporal correlations compared to traditional local Metropolis moves. By focusing on row-wise updates, the researchers circumvent the computational bottlenecks associated with full lattice contractions, maintaining a manageable computational complexity. Experiments demonstrate that this row-wise scheme effectively mitigates critical slowing down in the two-dimensional transverse-field Ising model, a crucial step towards accurate simulations of phase transitions. This achievement is particularly important as conventional methods struggle with the diverging autocorrelation times encountered near these critical points.

Furthermore, the research unveils improved optimization stability and lower ground-state energies when applied to the rugged landscape of the quantum spin glass. In systems plagued by frustrated interactions, where local updates often get trapped in suboptimal configurations, the autoregressive row-wise sampling allows for more efficient exploration of the phase space. The team benchmarked the algorithm on both the transverse-field Ising model and the quantum spin glass, providing compelling evidence of its effectiveness in diverse physical scenarios. These findings indicate that the proposed method offers a flexible and robust enhancement to existing PEPS-VMC methodologies.
This breakthrough establishes single-layer autoregressive row updates as a valuable algorithmic enhancement for PEPS-VMC, offering a pathway to more accurate and efficient simulations of strongly correlated two-dimensional systems. The work opens exciting possibilities for investigating complex quantum phenomena, including those found in materials science and condensed matter physics. By. By utilizing autoregressive single-layer row updates, the team generated collective, non-local configuration proposals, substantially reducing temporal correlations compared to traditional local Metropolis moves.

This innovative approach circumvents the computational bottlenecks associated with double-layer contractions, maintaining a manageable computational cost. Experiments benchmarked the algorithm on the two-dimensional transverse-field Ising model and a quantum spin glass, revealing significant improvements in performance. Results demonstrate that the row-wise scheme effectively mitigates critical slowing down near the Ising critical point, a crucial achievement for accurate simulations. Specifically, the team observed a marked reduction in autocorrelation times, indicating faster convergence towards the ground state.

Furthermore, in the complex energy landscape of the quantum spin glass, the new method yielded improved optimization stability and demonstrably lower ground-state energies. The study measured ground-state energies and optimization stability, finding that the autoregressive row-wise sampling consistently outperformed local PEPS-VMC sampling. Data shows that the single-layer autoregressive row updates provide a flexible and robust improvement to local PEPS-VMC sampling, offering a pathway to more advanced sampling schemes. The breakthrough delivers a method for generating collective, non-local configuration proposals with reduced computational cost, opening possibilities for simulating larger and more complex quantum systems.

Measurements confirm that this technique enhances the efficiency of variational optimization, particularly in challenging physical regimes. This work introduces a non-local sampling strategy restricted to single-row updates, yet extending beyond strictly local spin flips by enabling collective row-wise configuration changes. Crucially, the computational complexity remains comparable to standard local sampling strategies, making it a practical advancement for PEPS-VMC simulations. This method addresses limitations in standard PEPS-VMC algorithms, which often struggle with slow convergence and critical slowing down, especially when studying complex quantum systems. Researchers demonstrated the effectiveness of this row-wise scheme on the two-dimensional transverse-field Ising model and a spin glass, revealing significant improvements in mitigating critical slowing down near the Ising critical point.

Furthermore, the algorithm enhanced optimisation stability and achieved lower ground-state energies in the challenging landscape of the spin glass, suggesting a robust enhancement to existing PEPS-VMC methodologies. The authors acknowledge that while the method alleviates optimisation instability, it doesn’t entirely eliminate it in frustrated quantum systems. Future work could incorporate explicit constraints to enforce conserved quantities, enabling applications to more complex models like the doped 2D Hubbard model. Additionally, adapting the row-update paradigm to real-time schemes or isometric PEPS formulations may further enhance numerical stability, indicating that autoregressive sampling holds promise as a flexible component in future tensor-network approaches to strongly correlated quantum systems. This research establishes that carefully designed non-local sampling schemes can significantly benefit structured tensor-network states, suggesting the full potential of PEPS-based VMC remains to be explored.