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Charge order driven by nonlocal coulomb interactions in La3Ni2O7

DU Zhengzhong LI Jie LU Yi

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Charge order driven by nonlocal coulomb interactions in La3Ni2O7

DU Zhengzhong, LI Jie, LU Yi
cstr: 32037.14.aps.74.20250604
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  • The bilayer nickelate La3Ni2O7, a member of the Ruddlesden–Popper series, has recently received significant attention due to its superconductivity under high pressure (above 14 GPa) with a transition temperature of approximately 80 K. Its unique bilayer structure results in an electronic configuration significantly different from those observed in cuprates and infinite-layer nickelates. Consequently, understanding its correlated electronic structure and superconducting mechanism has become a topic of major scientific importance. Recent experimental observations have further identified the coexistence of charge and spin density wave orders in La3Ni2O7, suggesting a complex interplay between various competing electronic phases and superconductivity.In this work, the charge order in La3Ni2O7 is investigated using a low-energy effective model that explicitly includes the Ni-eg orbitals. By employing a combined density functional theory and dynamical mean-field theory (DFT+DMFT) framework, the influences of the nearest-neighbor Coulomb interaction V on charge ordering and electronic correlation effects are investigated, with nonlocal interactions treated at the Hartree approximation level. Our computational method features a newly developed tensor-network impurity solver, in which a natural-orbital basis and complex-time evolution are utilized, facilitating efficient and accurate evaluation of the Green's function on the real-frequency axis. Our analysis indicates that for interaction strengths below a critical value ($ V \leqslant V_{{\mathrm{c}}1} \approx 0.46 $ eV), the system retains sublattice symmetry, resulting in minimal changes of the spectral function. Several high-energy fine structures identified within the Hubbard bands correspond to the residual atomic multiplet excitations, enabling the extraction of effective Hubbard parameters. When $ V>V_{{\mathrm{c}}1} $, the sublattice symmetry is disrupted and the system transitions to a charge-ordered state. Spectral features systematically evolve with the increase of charge order, providing a clear benchmark for quantitatively evaluating the degree of charge disproportionation based on experimental data. The quasiparticle weight Z exhibits a nonmonotonic behavior with the increase of V, reaching a minimum value of nearly $ V \approx 0.60 $ eV in the more populated sublattice as it approaches half-filling. When the interaction further increases beyond $ V_{{\mathrm{c}}2} \approx 0.63 $ eV, the system becomes fully charged polarized, characterized by one sublattice becoming almost empty and the other substance being nearly three-quarters filled.These findings underscore the critical role of nonlocal Coulomb interactions in driving charge disproportionation and regulating electron correlation, thereby providing new insights into the low-energy ordering phenomena of bilayer nickelates.
      Corresponding author: LU Yi, yilu@nju.edu.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant No. 2022YFA1403000) and the National Natural Science Foundation of China (Grant No. 12274207)
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    Sun H L, Huo M W, Hu X W, Li J Y, Liu Z J, Han Y F, Tang L Y, Mao Z Q, Yang P T, Wang B S, Cheng J G, Yao D X, Zhang G M, Wang M 2023 Nature 621 493Google Scholar

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    Wang M, Wen H H, Wu T, Yao D X, Xiang T 2024 Chin. Phys. Lett. 41 077402Google Scholar

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    Keimer B, Kivelson S A, Norman M R, Uchida S, Zaanen J 2015 Nature 518 179Google Scholar

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    Botana A S, Norman M R 2020 Phys. Rev. X 10 011024

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    Luo Z H, Hu X W, Wang M, Wu W, Yao D X 2023 Phys. Rev. Lett. 131 126001Google Scholar

    [7]

    Zhang Y, Lin L F, Moreo A, Dagotto E 2023 Phys. Rev. B 108 L180510Google Scholar

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    Christiansson V, Petocchi F, Werner P 2023 Phys. Rev. Lett. 131 206501Google Scholar

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    LaBollita H, Pardo V, Norman M R, Botana A S 2024 arXiv: 2309.17279 [cond-mat.str-el]

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    Lechermann F, Gondolf J, Bötzel S, Eremin I M 2023 Phys. Rev. B 108 L201121Google Scholar

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    Shilenko D A, Leonov I V 2023 Phys. Rev. B 108 125105Google Scholar

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    Yang Y F, Zhang G M, Zhang F C 2023 Phys. Rev. B 108 L201108Google Scholar

    [16]

    Cao Y Y, Yang Y F 2024 Phys. Rev. B 109 L081105Google Scholar

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    Liu Y B, Mei J W, Ye F, Chen W Q, Yang F 2023 Phys. Rev. Lett. 131 236002Google Scholar

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    Shen Y, Qin M P, Zhang G M 2023 Chin. Phys. Lett. 40 127401Google Scholar

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    Yang Q G, Wang D, Wang Q H 2023 Phys. Rev. B 108 L140505Google Scholar

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    Zhang Y, Lin L F, Moreo A, Maier T A, Dagotto E 2024 Nat. Commun. 15 2470Google Scholar

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    Lu C, Pan Z M, Yang F, Wu C J 2024 Phys. Rev. Lett. 132 146002Google Scholar

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    Jiang K, Wang Z Q, Zhang F C 2024 Chin. Phys. Lett. 41 017402Google Scholar

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    Yang Y F 2025 Chin. Phys. Lett. 42 017301Google Scholar

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    Xue J R, Wang F 2024 Chin. Phys. Lett. 41 057403Google Scholar

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    Ghiringhelli G, Le Tacon M, Minola M, BlancoCanosa S, Mazzoli C, Brookes N, De Luca G, Frano A, Hawthorn D, He F Z, Loew T, Moretti Sala M, Peets D, Salluzzo M, Schierle E, Sutarto R, Sawatzky G, Weschke E, Keimer B, Braicovich L 2012 Science 337 821Google Scholar

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    Krieger G, Martinelli L, Zeng S, Chow L E, Kummer K, Arpaia R, Moretti Sala M, Brookes N B, Ariando A, Viart N, Salluzzo M, Ghiringhelli G, Preziosi D 2022 Phys. Rev. Lett. 129 027002Google Scholar

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    Liu Z, Huo M W, Li J, Li Q, Liu Y C, Dai Y M, Zhou X X, Hao J H, Lu Y, Wang M, Wen H H 2024 Nat. Commun. 15 7570Google Scholar

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    沈瑶 2024 物理学报 73 197104Google Scholar

    Shen Y 2024 Acta Phys.Sin. 73 197104Google Scholar

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    Zhao D, Zhou Y B, Huo M W, Wang Y, Nie L P, Yang Y, Ying J J, Wang M, Wu T, Chen X H 2025 Sci. Bull. 70 1239Google Scholar

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    Kakoi M, Oi T, Ohshita Y, Yashima M, Kuroki K, Kato T, Takahashi H, Ishiwata S, Adachi Y, Hatada N, Uda T, Mukuda H 2024 J. Phys. Soc. Jpn. 93 053702Google Scholar

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    Chen K W, Liu X Q, Jiao J C, Zou M Y, Jiang C Y, Li X, Luo Y X, Wu Q, Zhang N Y, Guo Y F, Shu L 2024 Phys. Rev. Lett. 132 256503Google Scholar

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    Chen X Y, Choi J, Jiang Z C, Mei J, Jiang K, Li J, Agrestini S, García-Fernández M, Sun H L, Huang X, Shen D W, Wang M, Hu J P, Lu Y, Zhou K J, Feng D L 2024 Nat. Commun. 15 9597Google Scholar

    [43]

    Wang G, Wang N N, Shen X L, Hou J, Ma L, Shi L F, Ren Z A, Gu Y D, Ma H M, Yang P T, Liu Z Y, Guo H Z, Sun J P, Zhang G M, Calder S, Yan J Q, Wang B S, Uwatoko Y, Cheng J G 2024 Phys. Rev. X 14 011040Google Scholar

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    Zhang Y N, Su D J, Huang Y N, Shan Z Y, Sun H L, Huo M W, Ye K X, Zhang J W, Yang Z H, Xu Y K, Su Y, Li R, Smidman M, Wang M, Jiao L, Yuan H Q 2024 Nat. Phys. 20 1269Google Scholar

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    Wang Y X, Jiang K, Wang Z Q, Zhang F C, Hu J P 2024 Phys. Rev. B 110 205122Google Scholar

    [46]

    Yi X W, Meng Y, Li J W, Liao Z W, Li W, You J Y, Gu B, Su G 2024 Phys. Rev. B 110 L140508Google Scholar

    [47]

    Chen X J, Jiang P H, Li J, Zhong Z C, Lu Y 2025 Phys. Rev. B 111 014515Google Scholar

    [48]

    Schollwöck U 2005 Rev. Mod. Phys. 77 259Google Scholar

    [49]

    Haegeman J, Cirac J I, Osborne T J, Pižorn I, Verschelde H, Verstraete F 2011 Phys. Rev. Lett. 107 070601Google Scholar

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    Haegeman J, Mariën M, Osborne T J, Verstraete F 2014 J. Math. Phys. 55 021902Google Scholar

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    Lu Y, Höppner M, Gunnarsson O, Haverkort M W 2014 Phys. Rev. B 90 085102Google Scholar

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    Lu Y, Cao X D, Hansmann P, Haverkort M W 2019 Phys. Rev. B 100 115134Google Scholar

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    Cao X D, Lu Y, Hansmann P, Haverkort M W 2021 Phys. Rev. B 104 115119Google Scholar

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    Cao X D, Lu Y, Stoudenmire E M, Parcollet O 2024 Phys. Rev. B 109 235110Google Scholar

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    Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15Google Scholar

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    Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685Google Scholar

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    Souza I, Marzari N, Vanderbilt D 2001 Phys. Rev. B 65 035109Google Scholar

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    Aryasetiawan F, Imada M, Georges A, Kotliar G, Biermann S, Lichtenstein A I 2004 Phys. Rev. B 70 195104Google Scholar

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    Mravlje J, Aichhorn M, Miyake T, Haule K, Kotliar G, Georges A 2011 Phys. Rev. Lett. 106 096401Google Scholar

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    Kugler F B, Zingl M, Strand H U R, Lee S S B, von Delft J, Georges A 2020 Phys. Rev. Lett. 124 016401Google Scholar

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  • 图 1  (a) DFT能带结构与Wannier投影低能能带(黑色实线)对比; (b) 轨道分辨的态密度

    Figure 1.  (a) Comparison between the DFT band structure and the low-energy Wannier-projected bands (black solid lines); (b) orbital-resolved density of states.

    图 2  $ V=0 $时 (a) 谱函数, 插图展示了谱函数中多重激发态特征结构的细节; (b)自能实部; (c) 自能虚部; (b), (c)虚线展示了两个轨道$ {\rm{Re}}\varSigma(\omega) \sim {\rm{Re}}\varSigma(0) + (1 - 1/Z)\omega $的线性拟合

    Figure 2.  For $ V=0 $: (a) Spectral function, inset shows the details of the multiplet excitations features; (b) real part of self energy; (c) imaginary part of self energy; dashed lines in (b), (c) show the linear fits of $ {\rm{Re}}\varSigma(\omega) \sim {\rm{Re}}\varSigma(0) + (1 - 1/Z)\omega $.

    图 3  子格点密度极化$ n_{{\rm{diff}}} $随近邻相互作用强度V的变化

    Figure 3.  Sublattice density polarization $ n_{{\rm{diff}}} $ as a function of nearest-neighbor interaction V.

    图 4  $ V=0 $与$ V=0.46 $的谱函数对比

    Figure 4.  Comparison of spectral functions for $ V=0 $ and $ V=0.46 $.

    图 5  谱函数在参数区间$ 0.48 \leqslant V \leqslant 0.56 $内的演化

    Figure 5.  Spectral functions in the parameter range $ 0.48 \leqslant V \leqslant 0.56 $.

    图 6  代表性V值的谱函数(上)与自能(下), 其中A(B)为多数(少数)占据格点, 内嵌图展示了下Hubbard带多峰结构的细节

    Figure 6.  Spectral functions (top) and self energies (bottom) for representative values of V, where A(B) denotes the majority (minority) occupied sublattice. Insets show the details of the lower Hubbard band features.

    图 7  重整化因子ZV增大的演化

    Figure 7.  Evolution of renormalization factor with increasing V

  • [1]

    Sun H L, Huo M W, Hu X W, Li J Y, Liu Z J, Han Y F, Tang L Y, Mao Z Q, Yang P T, Wang B S, Cheng J G, Yao D X, Zhang G M, Wang M 2023 Nature 621 493Google Scholar

    [2]

    Wang M, Wen H H, Wu T, Yao D X, Xiang T 2024 Chin. Phys. Lett. 41 077402Google Scholar

    [3]

    Lee P A, Nagaosa N, Wen X G 2006 Rev. Mod. Phys. 78 17Google Scholar

    [4]

    Keimer B, Kivelson S A, Norman M R, Uchida S, Zaanen J 2015 Nature 518 179Google Scholar

    [5]

    Botana A S, Norman M R 2020 Phys. Rev. X 10 011024

    [6]

    Luo Z H, Hu X W, Wang M, Wu W, Yao D X 2023 Phys. Rev. Lett. 131 126001Google Scholar

    [7]

    Zhang Y, Lin L F, Moreo A, Dagotto E 2023 Phys. Rev. B 108 L180510Google Scholar

    [8]

    Christiansson V, Petocchi F, Werner P 2023 Phys. Rev. Lett. 131 206501Google Scholar

    [9]

    Oh H, Zhang Y H 2023 Phys. Rev. B 108 174511Google Scholar

    [10]

    LaBollita H, Pardo V, Norman M R, Botana A S 2024 arXiv: 2309.17279 [cond-mat.str-el]

    [11]

    Lechermann F, Gondolf J, Bötzel S, Eremin I M 2023 Phys. Rev. B 108 L201121Google Scholar

    [12]

    Qu X Z, Qu D W, Chen J L, Wu C J, Yang F, Li W, Su G 2024 Phys. Rev. Lett. 132 036502Google Scholar

    [13]

    Shilenko D A, Leonov I V 2023 Phys. Rev. B 108 125105Google Scholar

    [14]

    Wu W, Luo Z H, Yao D X, Wang M 2024 Sci. China Phys. Mech. Astron 67 117402Google Scholar

    [15]

    Yang Y F, Zhang G M, Zhang F C 2023 Phys. Rev. B 108 L201108Google Scholar

    [16]

    Cao Y Y, Yang Y F 2024 Phys. Rev. B 109 L081105Google Scholar

    [17]

    Gu Y H, Le C C, Yang Z S, Wu X X, Hu J P 2023 arXiv: 2306.07275 [cond-mat.supr-con]

    [18]

    Liu Y B, Mei J W, Ye F, Chen W Q, Yang F 2023 Phys. Rev. Lett. 131 236002Google Scholar

    [19]

    Shen Y, Qin M P, Zhang G M 2023 Chin. Phys. Lett. 40 127401Google Scholar

    [20]

    Yang Q G, Wang D, Wang Q H 2023 Phys. Rev. B 108 L140505Google Scholar

    [21]

    Zhang Y, Lin L F, Moreo A, Maier T A, Dagotto E 2024 Nat. Commun. 15 2470Google Scholar

    [22]

    Lu C, Pan Z M, Yang F, Wu C J 2024 Phys. Rev. Lett. 132 146002Google Scholar

    [23]

    Fan Z, Zhang J F, Zhan B, Lv D S, Jiang X Y, Normand B, Xiang T 2024 Phys. Rev. B 110 024514Google Scholar

    [24]

    Jiang K, Wang Z Q, Zhang F C 2024 Chin. Phys. Lett. 41 017402Google Scholar

    [25]

    Xia C L, Liu H Q, Zhou S J, Chen H H 2025 Nat. Commun. 16 1054Google Scholar

    [26]

    Wang Y X, Zhang Y, Jiang K 2025 Chin. Phys. B 34 047105Google Scholar

    [27]

    Yang Y F 2025 Chin. Phys. Lett. 42 017301Google Scholar

    [28]

    Xue J R, Wang F 2024 Chin. Phys. Lett. 41 057403Google Scholar

    [29]

    Ghiringhelli G, Le Tacon M, Minola M, BlancoCanosa S, Mazzoli C, Brookes N, De Luca G, Frano A, Hawthorn D, He F Z, Loew T, Moretti Sala M, Peets D, Salluzzo M, Schierle E, Sutarto R, Sawatzky G, Weschke E, Keimer B, Braicovich L 2012 Science 337 821Google Scholar

    [30]

    Krieger G, Martinelli L, Zeng S, Chow L E, Kummer K, Arpaia R, Moretti Sala M, Brookes N B, Ariando A, Viart N, Salluzzo M, Ghiringhelli G, Preziosi D 2022 Phys. Rev. Lett. 129 027002Google Scholar

    [31]

    Tam C C, Choi J, Ding X, Agrestini S, Nag A, Wu M, Huang B, Luo H Q, Gao P, GarcíaFernández M, Qiao L, Zhou K J 2022 Nat. Mater. 21 1116Google Scholar

    [32]

    Rossi M, Osada M, Choi J, Agrestini S, Jost D, Lee Y, Lu H, Wang B Y, Lee K, Nag A, Chuang Y D, Kuo C T, Lee S J, Moritz B, Devereaux T P, Shen Z X, Lee J S, Zhou K J, Hwang H Y, Lee W S 2022 Nat. Phys. 18 869Google Scholar

    [33]

    Taniguchi S, Nishikawa T, Yasui Y, Kobayashi Y, Takeda J, Shamoto S i, Sato M 1995 J. Phys. Soc. Jpn. 64 1644Google Scholar

    [34]

    Seo D K, Liang W, Whangbo M H, Zhang Z, Greenblatt M 1996 Inorg. Chem. 35 6396Google Scholar

    [35]

    Wu G, Neumeier J J, Hundley M F 2001 Phys. Rev. B 63 245120Google Scholar

    [36]

    Liu Z J, Sun H L, Huo M W, Ma X Y, Ji Y, Yi E K, Li L S, Liu H, Yu J, Zhang Z Y, Chen Z Q, Liang F X, Dong H L, Guo H J, Zhong D Y, Shen B, Li S L, Wang M 2023 Sci. China Phys. Mech. Astron. 66 217411Google Scholar

    [37]

    Liu Z, Huo M W, Li J, Li Q, Liu Y C, Dai Y M, Zhou X X, Hao J H, Lu Y, Wang M, Wen H H 2024 Nat. Commun. 15 7570Google Scholar

    [38]

    沈瑶 2024 物理学报 73 197104Google Scholar

    Shen Y 2024 Acta Phys.Sin. 73 197104Google Scholar

    [39]

    Zhao D, Zhou Y B, Huo M W, Wang Y, Nie L P, Yang Y, Ying J J, Wang M, Wu T, Chen X H 2025 Sci. Bull. 70 1239Google Scholar

    [40]

    Kakoi M, Oi T, Ohshita Y, Yashima M, Kuroki K, Kato T, Takahashi H, Ishiwata S, Adachi Y, Hatada N, Uda T, Mukuda H 2024 J. Phys. Soc. Jpn. 93 053702Google Scholar

    [41]

    Chen K W, Liu X Q, Jiao J C, Zou M Y, Jiang C Y, Li X, Luo Y X, Wu Q, Zhang N Y, Guo Y F, Shu L 2024 Phys. Rev. Lett. 132 256503Google Scholar

    [42]

    Chen X Y, Choi J, Jiang Z C, Mei J, Jiang K, Li J, Agrestini S, García-Fernández M, Sun H L, Huang X, Shen D W, Wang M, Hu J P, Lu Y, Zhou K J, Feng D L 2024 Nat. Commun. 15 9597Google Scholar

    [43]

    Wang G, Wang N N, Shen X L, Hou J, Ma L, Shi L F, Ren Z A, Gu Y D, Ma H M, Yang P T, Liu Z Y, Guo H Z, Sun J P, Zhang G M, Calder S, Yan J Q, Wang B S, Uwatoko Y, Cheng J G 2024 Phys. Rev. X 14 011040Google Scholar

    [44]

    Zhang Y N, Su D J, Huang Y N, Shan Z Y, Sun H L, Huo M W, Ye K X, Zhang J W, Yang Z H, Xu Y K, Su Y, Li R, Smidman M, Wang M, Jiao L, Yuan H Q 2024 Nat. Phys. 20 1269Google Scholar

    [45]

    Wang Y X, Jiang K, Wang Z Q, Zhang F C, Hu J P 2024 Phys. Rev. B 110 205122Google Scholar

    [46]

    Yi X W, Meng Y, Li J W, Liao Z W, Li W, You J Y, Gu B, Su G 2024 Phys. Rev. B 110 L140508Google Scholar

    [47]

    Chen X J, Jiang P H, Li J, Zhong Z C, Lu Y 2025 Phys. Rev. B 111 014515Google Scholar

    [48]

    Schollwöck U 2005 Rev. Mod. Phys. 77 259Google Scholar

    [49]

    Haegeman J, Cirac J I, Osborne T J, Pižorn I, Verschelde H, Verstraete F 2011 Phys. Rev. Lett. 107 070601Google Scholar

    [50]

    Haegeman J, Mariën M, Osborne T J, Verstraete F 2014 J. Math. Phys. 55 021902Google Scholar

    [51]

    Lu Y, Höppner M, Gunnarsson O, Haverkort M W 2014 Phys. Rev. B 90 085102Google Scholar

    [52]

    Lu Y, Cao X D, Hansmann P, Haverkort M W 2019 Phys. Rev. B 100 115134Google Scholar

    [53]

    Cao X D, Lu Y, Hansmann P, Haverkort M W 2021 Phys. Rev. B 104 115119Google Scholar

    [54]

    Cao X D, Lu Y, Stoudenmire E M, Parcollet O 2024 Phys. Rev. B 109 235110Google Scholar

    [55]

    Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15Google Scholar

    [56]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [57]

    Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685Google Scholar

    [58]

    Marzari N, Vanderbilt D 1997 Phys. Rev. B 56 12847Google Scholar

    [59]

    Souza I, Marzari N, Vanderbilt D 2001 Phys. Rev. B 65 035109Google Scholar

    [60]

    Aryasetiawan F, Imada M, Georges A, Kotliar G, Biermann S, Lichtenstein A I 2004 Phys. Rev. B 70 195104Google Scholar

    [61]

    Mravlje J, Aichhorn M, Miyake T, Haule K, Kotliar G, Georges A 2011 Phys. Rev. Lett. 106 096401Google Scholar

    [62]

    Kugler F B, Zingl M, Strand H U R, Lee S S B, von Delft J, Georges A 2020 Phys. Rev. Lett. 124 016401Google Scholar

    [63]

    Georges A, Medici L d, Mravlje J 2013 Annu. Rev. Condens. Matter Phys. 4 137Google Scholar

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Metrics
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Publishing process
  • Received Date:  08 May 2025
  • Accepted Date:  27 May 2025
  • Available Online:  04 June 2025
  • Published Online:  05 September 2025
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