In the realm of quantum physics and energy materials research, understanding the behavior of strongly correlated quantum many-body systems is crucial. These systems are complex and require sophisticated tools for simulation. Among these tools, tensor network states have emerged as indispensable. Researchers like Thomas Barthel, affiliated with the University of Pittsburgh, have been at the forefront of developing and applying these methods.
Tensor network states, particularly tree tensor network states (TTNS), have been successfully used for simulating two-dimensional systems and benchmarking quantum simulation approaches in various fields, including condensed matter, nuclear, and particle physics. Compared to the more traditional matrix product states (MPS), TTNS can significantly reduce the graph distance of physical degrees of freedom. However, recent research by Barthel has revealed a surprising finding: for large systems in dimensions greater than one, MPS simulations of low-energy states are more efficient than TTNS simulations.
The study, published in the journal Physical Review B, focuses on two and three-dimensional systems. It determines the scaling of computational costs for different boundary conditions under the assumption that the system obeys an entanglement area law. This law implies that bond dimensions scale exponentially with the surface area of the associated subsystems. The research provides valuable insights into the computational efficiency of different tensor network states, which can have practical applications in the energy sector, particularly in the development of quantum materials and technologies.
Understanding the computational costs and efficiencies of these simulations is crucial for advancing quantum research and development. For the energy industry, this research could lead to more efficient and accurate simulations of quantum materials, which are essential for developing new energy technologies, such as advanced batteries, solar cells, and quantum computers. By optimizing the computational methods used in these simulations, researchers can accelerate the discovery and development of new energy materials and technologies.
This article is based on research available at arXiv.