A new approach for a quantitative description of strongly correlated materials

BY: Daan Vrancken, Simon, Ganne, Daan Verraes, Tom Braeckevelt, Lukas Devos, Laurens Vanderstraeten, Jutho Haegeman, and Veronique Van Speybroeck

In condensed matter physics, a quantitative description of the properties of novel materials is a key step towards their use in innovative technologies, ranging from next-generation electronics to quantum devices. This is especially true for strongly correlated materials, a class of substances where the strong interactions between electrons give rise to exotic properties. For example, materials like high-temperature superconductors, which can conduct electricity with no resistance, fall into this category. However, accurately modeling these systems has been a major challenge for traditional computational methods, as the strong electron correlations make their behavior notoriously difficult to predict.

Figure 1: Image concept of a magnet levitating above a high-temperature superconductor. Credit: KTSDesign/Science Photo Library

This research, carried out in close collaboration between the Center for Molecular Modeling (CMM) and the Quantum Group at Ghent University, presents a powerful new computational tool to overcome this challenge. The method combines the complementary expertise of the two groups: the CMM’s strength in Density Functional Theory (DFT) and the Quantum Group’s specialization in Tensor Networks. This hybrid framework allows for a highly accurate description of a material's electronic structure, enabling the precise prediction of key properties like its band gap, a crucial measure of its ability to conduct electricity.

The procedure, illustrated in Figure 2, begins with a DFT calculation to obtain an initial description of the material. DFT is a widely used method in computational physics and chemistry that simplifies the many-body problem of a system of interacting electrons into a problem of a single electron moving in an effective potential. Applying the constrained random phase approximation (cRPA) results in a "downfolded" model, which is a simplified, yet highly effective, representation of the material that captures the essential physics of the electron correlations. This model is then solved using tensor networks, a mathematical engine that can efficiently describe the intricate quantum states of many-body systems. 

Figure 2: Schematic representation of the numerical procedure. From an initial DFT calculation, a subspace (orange bands) is selected to construct an effective model via downfolding. The model is solved using tensor networks.

The effectiveness of this approach was validated by applying it to several one-dimensional and quasi-one-dimensional materials, including conjugated polymers and the quasi-one-dimensional charge-transfer insulator Sr2​CuO3​ , which is related to high-temperature superconductors. For these materials, the predicted electronic band gaps showed excellent agreement with both state-of-the-art computational techniques and experimental data. This demonstrates the method's ability to provide a quantitative and accurate description of strongly correlated materials.

The use of tensor networks also provides a way to access other important physical properties beyond the band gap, such as spin magnetization and various excitation energies, offering a more complete picture of the material's behavior. The success of this framework presents a new and indispensable tool in the computational material design toolbox for understanding and predicting the properties of strongly correlated materials, offering a new path forward in modeling complex systems. The scalability of the tensor network approach makes it particularly promising for future studies of even larger and more complex materials.

How VSC contributed to the work

"Both the downfolding and tensor network simulations are complex and computationally heavy calculations. The resources provided by the Flemish Supercomputer Center have been essential to obtaining high-quality results.”

Read the full publication in ACS here

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