Ipeps Accurately Computes Energy Variance, Enabling Ground-State Energy Extrapolation to Zero-Variance Limit

Understanding the energy fluctuations within complex materials represents a significant challenge in condensed matter physics, yet accurately calculating these fluctuations is crucial for determining a system’s true ground state and identifying potential phase transitions. Emilio Cortés Estay, Naushad A. Kamar, and Philippe Corboz, all from the Institute for Theoretical Physics at the University of Amsterdam, now present a method for precisely computing the energy variance of two-dimensional systems using infinite projected entangled-pair states, or iPEPS. Their approach, which involves a sophisticated tensor network contraction technique, substantially improves upon existing methods and allows for reliable extrapolations to the true ground state energy. The team demonstrates the power of this technique by successfully applying it to several benchmark models, including the Heisenberg and Shastry-Sutherland models, and extends it to analyse open systems and locate phase transitions in dissipative systems like the Ising model, offering a powerful new tool for exploring complex quantum phenomena.

Infinite Projected Entangled Pair States Development

This is a comprehensive collection of references concerning tensor network states, particularly infinite projected entangled pair states, and their applications to condensed matter physics, with a strong focus on the Shastry-Sutherland model. The compilation covers core concepts, algorithmic developments, and applications to understanding complex quantum systems. I. Core Concepts and Algorithms (TNS and iPEPS) * Fundamentals of TNS: The list begins with foundational papers establishing the theoretical basis for representing quantum many-body states efficiently. * iPEPS Algorithm Development: A significant portion focuses on optimizing the iPEPS algorithm itself, including techniques for efficient contraction of the tensor network to calculate observable properties like energy and correlation functions.

This includes exploring different update strategies, gauge fixing methods, and symmetry implementations to reduce computational cost and improve accuracy. * Time Evolution and Steady States: The collection also covers algorithms for simulating the time evolution of iPEPS and finding steady states of dissipative systems, utilizing differentiable programming techniques for optimization. * Variational Methods: Papers detail the use of variational principles to find ground states and steady states. II. Applications to the Shastry-Sutherland Model * Ground State Properties: A large number of references focus on using iPEPS to study the ground state of the Shastry-Sutherland model, determining its different phases, investigating quantum phase transitions, and searching for evidence of spin liquid behavior.

• Comparison with Other Methods: The list includes papers comparing iPEPS results with those obtained from other numerical methods and experimental studies. III. Beyond Static Properties: Dynamics and Dissipation * Time-Dependent iPEPS: Algorithms for simulating the time evolution of iPEPS are presented. * Dissipative Systems: The application of iPEPS to study open quantum systems with dissipation, such as driven-dissipative Rydberg gases, is detailed. * Steady State Properties: Methods for finding and characterizing the steady states of dissipative systems are included.

IV. Specific Techniques and Tools * Generating Functions: The use of generating functions to simplify the summation of tensor network diagrams is explored. * Correlation Functions: Efficient methods for calculating correlation functions with iPEPS are presented. * Software and Libraries: References to software packages and libraries for performing TNS calculations are provided. Key Takeaways and Significance: * Comprehensive Coverage: This list provides a thorough overview of the field of iPEPS and its applications.

• Focus on the Shastry-Sutherland Model: The Shastry-Sutherland model serves as a benchmark system for testing and developing iPEPS algorithms. * Cutting-Edge Research: The list includes many recent papers, reflecting the ongoing development of the field. * Bridging Theory and Experiment: The research aims to provide insights into the behavior of real materials and to guide experimental studies. In essence, this is a valuable resource for anyone interested in learning about tensor network states, their applications to condensed matter physics, and the study of strongly correlated quantum systems. The detailed list of references allows researchers to delve deeper into specific topics and to build upon the existing body of knowledge.

Accurate Energy Variance in Quantum Systems

Scientists have developed a new method to accurately compute the energy variance within infinite projected entangled-pair states, a powerful technique for studying two-dimensional quantum systems. This advancement enables systematic improvements in determining the ground-state energy with unprecedented precision, crucial for understanding complex materials and quantum phenomena. The work centers on a sophisticated contraction algorithm, utilizing the corner transfer matrix renormalization group method, to evaluate correlations between Hamiltonian terms within a large network of tensors. Experiments demonstrate that this approach significantly improves accuracy compared to previous methods, and researchers successfully applied the technique to the Heisenberg model, a free fermionic system, and the Shastry-Sutherland model, confirming the utility of variance extrapolation for refining energy calculations.

The team measured the energy variance for the Heisenberg model, achieving a level of precision previously unattainable, and observed similar improvements in the other models tested. Furthermore, the study extends this method to open quantum systems, employing the Liouvillian to assess the quality of steady-state solutions and identify first-order phase transitions. Using the dissipative Ising model as an example, scientists computed a measure of the system’s closeness to its steady state, demonstrating its effectiveness in locating phase transitions. The algorithm achieves this accuracy by substantially reducing the required computational resources, making it tractable even for large systems. This breakthrough delivers a powerful new capability for exploring the behavior of complex quantum systems and promises to accelerate progress in fields such as materials science and quantum computing.

Variance Extrapolation Improves Energy Calculations Significantly

Scientists have developed a new approach to accurately calculate the energy variance of infinite projected entangled-pair states, a powerful technique for studying two-dimensional many-body systems. This method involves evaluating correlations between Hamiltonian terms within a large network using the corner transfer matrix renormalization group, allowing for systematic improvements in the ground-state energy estimation. Results demonstrate substantially higher accuracy compared to previous methods, enabling precise calculations even with complex systems. The researchers successfully applied this variance extrapolation to several models, including the Heisenberg model, a free fermionic system, and the Shastry-Sutherland model, achieving results consistent with established methods like quantum Monte Carlo and exact calculations. Furthermore, they extended the approach to study open quantum systems, demonstrating its ability to assess the quality of steady-state solutions and identify first-order phase transitions, exemplified by the dissipative quantum Ising model. This advancement provides a practical tool for investigating phase diagrams of open quantum systems and refining representations of steady states, promising further insights into complex quantum phenomena.