Research 研究

We develop ab initio numerical approaches to simulate and study the properties of strongly correlated quantum materials, e.g., unconventional superconductivity, correlated topological materials, and exotic phase transitions. In particular, we focus on merging the predictive power of density functional theory (DFT) and the high accuracy of quantum embedding approaches (QE), aiming to simulate the properties of the correlated quantum materials reliably from the first principle. 

我們的團隊致力於發展有效的第一原理多體方法來了解關聯性量子材料的物理特性，包括非常規超導現象，強關聯拓樸材料，以及量子材料中的相變。我們發展的方法結合密度泛函理論的材料性質預測能力以及量子鑲嵌方法描述強關聯現象的能力，能有效及準確的預測關聯性量子材料的物理現象。


Quantum Embedding Theory 量子鑲嵌理論

Quantum embedding (QE) approaches are accurate quantum many-body methods to simulate strongly correlated systems, e.g., Mott insulator, heavy fermion, and unconventional superconductors. They are based on a common idea of partitioning the crystal lattice systems into an atom or a molecule surrounded by an effective medium formed by the other atoms (see Fig. 1). This allows one to map the original lattice problem into an effective impurity model described by the embedding Hamiltonian. The embedding Hamiltonian can be solved using exact-diagonalization techniques to obtain the ground state and excited state properties. The local strong correlated phenomena, e.g., Mott metal-insulator transition and heavy fermion phenomena, can be described reliably by the embedding Hamiltonian. There are several QE theories, including dynamical mean-field theory (DMFT) [1], density matrix embedding theory (DMET) [2,3], and rotationally-invariant slave-boson theory (RISB) [2-5], that belong to the family of QE approaches. Our research focuses on the advances and applications of these QE methods to quantum materials.

量子鑲嵌理論是量子多體方法的一個分支，可以準確的模擬強關聯電子系統的物理現象，例如莫特絕緣體，重費米子，以及非常規超導現象。其共同的概念是將晶格系統畫分出一個區塊的原子或是分子，而晶格中其餘的原子被當作有效的環境(見Fig.1)。這個有效模型可以更進一步地轉換成量子雜質模型，稱為鑲嵌漢密頓量。這個鑲嵌漢密頓量可以被嚴格的對角化，得到其基態及激發態，並有效的描述局域原子或分子的強關聯現象，例如莫特金屬相變，及重費米子現象。至今，最有名的量子鑲嵌理論包含了，動態平均場論[1]，密度矩陣鑲嵌理論[2,3]，以及旋轉不變使役波色子場論[2-5]。我們的研究專注於這類方法的進階發展以及量子材料上的應用。

Figure 1: quantum Embedding --- mapping a lattice problem to a small impurity model described by the embedding Hamiltonian.

Reference (參考論文):

[1] A. Georges; G. Kotliar; W. Krauth; M. Rozenberg. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. 

       Reviews of Modern Physics. 68 (1): 13, 1996.

[2] Thomas Ayral, Tsung-Han Lee, and Gabriel Kotliar, Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a 

       Unified Perspective, Physical Review B 96 (23), 235139. 2017.

[3] Tsung-Han Lee, Thomas Ayral, Yong-Xin Yao, Nicola Lanatà, Gabriel Kotliar, Rotationally invariant slave-boson and density matrix embedding theory: Unified 3. 

       framework and comparative study on the one-dimensional and two-dimensional Hubbard model, Physical Review B 99 (11), 115129. 2019.

[4] Tsung-Han Lee, Corey Melnick, Ran Adler, Nicola Lanatà, Gabriel Kotliar, Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard 

       models and realistic materials, Phys. Rev. B 108, 245147, 2023

[5] Tsung-Han Lee, Nicola Lanatà, Gabriel Kotliar, Accuracy of ghost-rotationally-invariant slave-boson and dynamical mean field theory as a function of the impurity

       model bath size, Physical Review B 107, L121104, 2023.

Density Functional Theory Plus Quantum Embedding Theory 結合密度泛函和量子鑲嵌理論

The quantum embedding (QE) approaches can be combined with density functional theory (DFT) to simulate the properties of correlated quantum materials. It is often called DFT+QE approaches, e.g., DFT+dynamical mean-field theory (DFT+DMFT) and DFT+rotationally-invariant slave-boson (DFT+RISB). We have developed and applied these approaches to several correlated materials to validate the accuracy of these methods. Figure 2 shows the accuracy of the DFT+RISB in capturing the crystal structure and electronic properties of the transition metal oxides, significantly improving the DFT (LDA) results [6]. Ｗe have also applied DFT+RISB to Lanthanide metals, capturing accurate lattice parameters [7].


量子鑲嵌理論可以跟密度泛函理論結合來模擬強關聯量子材料的性質。我們通常稱此類方法為DFT+QE，例如DFT+DMFT(動態平均場論)和DFT+RISB(使役波色子場論)。 我們發展並應用這兩套方法到強關聯過度金屬氧化物上來驗證他們能夠準確得到實驗上觀測到的晶格結構，並改善DFT (LDA)無法準確描述晶格結構的缺點(見Fig. 2) [6]。此外，我們也應用此方法到重費米錒系金屬上，並準確地得到實驗觀測到的晶格常數 [7]。

Figure 2: DFT(LDA)+RISB reliabily cpatures the crystal structures and lattice parameters for transition metal oxides. 

Reference (參考論文):

[6] Nicola Lanatà, Tsung-Han Lee, Yong-Xin Yao, Vladan Stevanovic and Vladimir Dobrosavljevic, Connection between Mott physics and 

       crystal structure in a series of transition metal binary compounds, npj Computational Materials 5 (1), 30. 2019.

[7] John Rogers, Tsung-Han Lee, Sahar Pakdel, Wenhu Xu, Vladimir Dobrosavljevic, Yong-Xin Yao, Ove Christiansen, and Nicola Lanatà, 

       Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning, 

       Physical Review Research 3, 013101. 2021.

Ongoing and future directions 目前及未來研究方向

Our group's current goal is to continue developing the above QE approaches to simulate correlated quantum material's:

We welcome enthusiastic students to contact the PI for further information.


我們團隊目前的研究方向為發展量子鑲嵌方法來模擬關聯性量子材料的:

歡迎對理論凝聚態物理及程式編譯有興趣的同學與我們聯絡。