| Lin H Y, Guo Y, He R Q, Xie Z Y and Lu Z Y 2024 Phys. Rev. B 109 235133 |
| Trivedi N and Ceperley D M 1989 Phys. Rev. B 40 2737 |
| Trivedi N and Ceperley D M 1990 Phys. Rev. B 41 4552 |
| Verstraete F, Murg V and Cirac J I 2008 Adv. Phys. 57 143 |
| Orús R 2019 Nature Reviews Physics 1 538 |
| Cirac J I, Pérez-García D, Schuch N and Verstraete F 2021 Rev. Mod. Phys. 93 045003 |
| Bañuls M C 2023 Annu. Rev. Condens. Matter Phys. 14 173 |
| Xiang T 2023 Density Matrix and Tensor Network Renormalization (Cambridge University Press) |
| Nightingale M P and Umrigar C J 1998 Quantum Monte Carlo methods in physics and chemistry (Springer Science & Business Media) |
| Becca F and Sorella S 2017 Quantum Monte Carlo Approaches for Correlated Systems (Cambridge University Press) p. 167 |
| ten Haaf D F B, van Bemmel H J M, van Leeuwen J M J, van Saarloos W and Ceperley D M 1995 Phys. Rev. B 51 13039 |
| Sorella S and Capriotti L 2000 Phys. Rev. B 61 2599 |
| Reynolds P J, Ceperley D M, Alder B J and Lester W A 1982 The Journal of Chemical Physics 77 5593 |
| Montangero S 2018 Introduction to Tensor Network Methods (Springer Nature) Chaps. 5 and 6 |
| Verstraete F and Cirac J I arXiv:cond-mat/0407066 |
| Orús R 2014 Ann. Phys. 349 117 |
| Xie Z Y, Liao H J, Huang R Z, Xie H D, Chen J, Liu Z Y and Xiang T 2017 Phys. Rev. B 96 045128 |
| Yang L P, Fu Y F, Xie Z Y and Xiang T 2023 Phys. Rev. B 107 165127 |
| Orús R 2014 Eur. Phys. J. B 87 280 |
| du Croo de Jongh M S L, van Leeuwen J M J and van Saarloos W 2000 Phys. Rev. B 62 14844 |
| Clark B K and Changlani H J arXiv:1404.2296 |
| Wouters S, Verstichel B, Van Neck D and Kin-Lic Chan G 2014 Phys. Rev. B 90 045104 |
| Qin M P 2020 Phys. Rev. B 102 125143 |
| Lin H Y, He R Q and Lu Z Y 2022 Chin. Phys. B 31 080203 |
| Zhang G M, Hu H and Yu L 2003 Phys. Rev. Lett. 91 067201 |
| Mezzacapo F 2012 Phys. Rev. B 86 045115 |
| Jiang H C, Yao H and Balents L 2012 Phys. Rev. B 86 024424 |
| Hu W J, Becca F, Parola A and Sorella S 2013 Phys. Rev. B 88 060402 |
| Morita S, Kaneko R and Imada M 2015 J. Phys. Soc. Jpn. 84 024720 |
| Wang L and Sandvik A W 2018 Phys. Rev. Lett. 121 107202 |
| Ferrari F and Becca F 2020 Phys. Rev. B 102 014417 |
| Liu W Y, Gong S S, Li Y B, Poilblanc D, Chen W Q and Gu Z C 2022 Science Bulletin 67 1034 |
| Wang L, Poilblanc D, Gu Z C, Wen X G and Verstraete F 2013 Phys. Rev. Lett. 111 037202 |
| Liu W Y, Dong S, Wang C, Han Y, An H, Guo G C and He L 2018 Phys. Rev. B 98 241109 |
| Schulz H J, Ziman T A L and Poilblanc D 1996 Journal de Physique I 6 675 |
| Choo K, Neupert T and Carleo G 2019 Phys. Rev. B 100 125124 |
| Nomura Y and Imada M 2021 Phys. Rev. X 11 031034 |
| Anderson J B 1975 The Journal of Chemical Physics 63 1499 |
| Verstraete F, Porras D and Cirac J I 2004 Phys. Rev. Lett. 93 227205 |
| Liao H J, Liu J G, Wang L and Xiang T 2019 Phys. Rev. X 9 031041 |
| Xie Z Y, Chen J, Qin M P, Zhu J W, Yang L P and Xiang T 2012 Phys. Rev. B 86 045139 |
| Buonaura M C and Sorella S 1998 Phys. Rev. B 57 11446 |
| Sandvik A W 1997 Phys. Rev. B 56 11678 |
| Néel L 1936 Ann. Phys. 11 232 |
| Néel L 1932 J. Phys. Radium 3 160 |
| Singh R R P, Zheng W H, Hamer C J and Oitmaa J 1999 Phys. Rev. B 60 7278 |
| Takano K, Kito Y, Ōno Y and Sano K 2003 Phys. Rev. Lett. 91 197202 |
| Mambrini M, Läuchli A, Poilblanc D and Mila F 2006 Phys. Rev. B 74 144422 |
| Darradi R, Derzhko O, Zinke R, Schulenburg J, Krüger S E and Richter J 2008 Phys. Rev. B 78 214415 |
| Murg V, Verstraete F and Cirac J I 2009 Phys. Rev. B 79 195119 |
| Haghshenas R and Sheng D N 2018 Phys. Rev. B 97 174408 |
| Hasik J, Poilblanc D and Becca F 2021 SciPost Phys. 10 012 |
| Qian X J and Qin M P 2024 Phys. Rev. B 109 L161103 |
| Zhitomirsky M E and Ueda K 1996 Phys. Rev. B 54 9007 |
| Capriotti L and Sorella S 2000 Phys. Rev. Lett. 84 3173 |
| Isaev L, Ortiz G and Dukelsky J 2009 Phys. Rev. B 79 024409 |
| Yu J F and Kao Y J 2012 Phys. Rev. B 85 094407 |
| Doretto R L 2014 Phys. Rev. B 89 104415 |
| Chubukov A V and Jolicoeur T 1991 Phys. Rev. B 44 12050 |
| Gong S S, Zhu W, Sheng D N, Motrunich O I and Fisher M P A 2014 Phys. Rev. Lett. 113 027201 |
| Zhang X Y, Chi R Z, Liu Y and Wang L 2024 Phys. Rev. B 109 075129 |
| A direct power fitting of the data in Fig. 3 gives extrapolated values -0.50376(4) (J2 = 0.5) and -0.49506(55) (J2 = 0.55) in the large-D limit, which agree very well the exact values -0.50381 and -0.495178 in Ref. |
| . |
| Chen A and Heyl Markus 2024 Nat. Phys. 20 1476 |
| Ledinauskas E and Anisimovas E 2023 SciPost Phys. 15 229 |
| Szabó A and Castelnovo C 2020 Phys. Rev. Res. 2 033075 |
| Liang X, Liu W Y, Lin P Z, Guo G C, Zhang Y S and He L 2018 Phys. Rev. B 98 104426 |
| Wang J Q, Wu H Q, He R Q and Lu Z Y 2024 Phys. Rev. B 109 245120 |
| Ferrari F, Becca F and Carrasquilla J 2019 Phys. Rev. B 100 125131 |
| Reh M, Schmitt M and Gärttner M 2023 Phys. Rev. B 107 195115 |
| Chen H, Hendry D, Weinberg P and Feiguin A 2023 Advances in Neural Information Processing Systems (Curran Associates, Inc.) pp. 7490-7503 |
| Li M, Chen J, Xiao Q, Wang F, Jiang Q, Zhao X, Lin R, An H, Liang X and He L 2022 IEEE Transactions on Parallel and Distributed Systems 33 2846 |
| Liang X, Dong S J and He L 2021 Phys. Rev. B 103 035138 |
| Liang X, Li M, Xiao Q, Chen J, Yang C, An H and He L 2023 Machine Learning: Science and Technology 4 015035 |
| Rende R, Viteritti L L, Bardone L, Becca F and Goldt S arXiv:2310.05715 |
| Chen B B, Gao Y, Guo Y B, Liu Y, Zhao H H, Liao H J, Wang L, Xiang T, Li W and Xie Z Y 2020 Phys. Rev. B 101 220409 |
| Xie Z Y, Chen J, Yu J F, Kong X, Normand B and Xiang T 2014 Phys. Rev. X 4 011025 |
| Sandvik A W and Vidal G 2007 Phys. Rev. Lett. 99 220602 |
| Liu W Y, Huang Y Z, Gong S S and Gu Z C 2021 Phys. Rev. B 103 235155 |