Tackling the Exponential Wall in Strongly Correlated Materials Simulations: A Quantum Embedding Perspective

Simulating strongly correlated materials accurately presents an intriguing challenge in condensed matter physics. These materials exhibit strong electron interactions, characterized by intricate entangled states that elude description through conventional mean-field single-particle methods, such as density functional theory (DFT). Representing these entangled states makes it necessary to utilize many-body techniques and wavefunctions, whose computational complexity grows exponentially with the number of orbitals in the materials, known as the "exponential wall problem."

In this colloquium, I will discuss the journey to unravel this intricate problem, guided by the concept of quantum embedding. This concept envisions materials as atoms or molecules embedded within an effective medium, representing the remaining atoms in the material, and the form of this effective medium is self-consistently determined. I will explore two distinct but complementary approaches based on quantum embedding: the dynamical mean-field theory (DMFT) [1], renowned for its precision, and the rotationally-invariant slave boson (RISB) [2], celebrated for its computational efficiency. We will delve deep into the advantages and limitations of these two methodologies when applied to correlated materials [3,4].

Furthermore, I will introduce a systematic methodology to enhance the accuracy of RISB by introducing auxiliary ghost orbitals, a technique we term "ghost-rotationally-invariant slave-boson" (g-RISB) or the "ghost-Gutzwiller approximation" [5,6,7]. This approach offers flexibility to balance accuracy and efficiency when simulating strongly correlated systems, providing a systematic route to address the exponential wall problem.

References:
[1] Antoine Georges, Gabriel Kotliar, Werner Krauth, and Marcelo J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)
[2] F. Lechermann, A. Georges, G. Kotliar, and O. Parcollet, Phys. Rev. B 76, 155102 (2007)
[3] Nicola Lanatà, Yongxin Yao, Cai-Zhuang Wang, Kai-Ming Ho, and Gabriel Kotliar, Phys. Rev. X 5, 011008 (2015)
[4] Nicola Lanatà, Tsung-Han Lee, Yong-Xin Yao, Vladan Stevanović, Vladimir Dobrosavljević, npj Computational Materials 5 (1), 1-6 (2019)
[5] Nicola Lanatà, Tsung-Han Lee, Yong-Xin Yao, and Vladimir Dobrosavljević, Phys. Rev. B 96, 195126 (2017)
[6] Tsung-Han Lee, Nicola Lanatà, and Gabriel Kotliar, Phys. Rev. B 107, L121104 (2023)
[7] Tsung-Han Lee, Corey Melnick, Ran Adler, Nicola Lanatà, Gabriel Kotliar, arXiv:2305.11128 (2023)