| COMPUTATIONAL PROGRAMS FOR PHYSICS |
Prev
Next
|
|
|
Accurate quantum critical points and nonlocal string order parameters in the spin tetrahedron chain |
| Zhi-Yong Wu(吴志勇), Kai-Ming Zhang(张凯铭), and Li-Xiang Cen(岑理相)† |
| Center of Theoretical Physics, College of Physics, Sichuan University, Chengdu 610065, China |
|
|
|
|
Abstract The ground-state phase diagram and nonlocal order parameters of an infinite spin tetrahedron chain with inhomogeneous exchange couplings are investigated. It is shown that the phase boundaries of the three phases in the model can be determined precisely, in line with the precision of its ground-state energy. Numerical calculations using the regularized time-evolving block decimation (rTEBD) algorithm yield the locations of the two quantum critical points with an accuracy about 10 digits. Moreover, we explain how to calculate the parity-associated string order for the output wave function obtained through the rTEBD procedure, which not only reveals the presence of long-range correlations but also identifies the symmetry-protected topological order within the intermediate phase of the model.
|
Received: 16 July 2025
Revised: 25 September 2025
Accepted manuscript online: 29 September 2025
|
|
PACS:
|
75.10.Jm
|
(Quantized spin models, including quantum spin frustration)
|
| |
75.10.Pq
|
(Spin chain models)
|
| |
64.70.Tg
|
(Quantum phase transitions)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12471443). |
Corresponding Authors:
Li-Xiang Cen
E-mail: lixiangcen@scu.edu.cn
|
Cite this article:
Zhi-Yong Wu(吴志勇), Kai-Ming Zhang(张凯铭), and Li-Xiang Cen(岑理相) Accurate quantum critical points and nonlocal string order parameters in the spin tetrahedron chain 2025 Chin. Phys. B 34 117502
|
[1] Sachdev S 2011 Quantum Phase Transitions (Cambridge: Cambridge University Press)
[2] Carr L D E 2010 Understanding Quantum Phase Transitions (Boca Raton: Taylor and Francis)
[3] Sadler L E, Higbie J M, Leslie S R, Vengalattore M and Stamper-Kurn D M 2006 Nature 443 312
[4] Lian H L 2012 Chin. Phys. C 36 479
[5] Dag C B, Wang Y, Uhrich P, Na X and Halimeh J C 2023 Phys. Rev. B 107 L121113
[6] Heyl M, Polkovnikov A and Kehrein S 2013 Phys. Rev. Lett. 110 135704
[7] Gorin T, Prosen T, Seligman T H and Znidaric M 2006 Phys. Rep. 435 33
[8] Quan H T, Song Z, Liu X F, Zanardi P and Sun C P 2006 Phys. Rev. Lett. 96 140604
[9] Jafari R and Johannesson H 2017 Phys. Rev. Lett. 118 015701
[10] Fernández-Lorenzo S and Porras D 2017 Phys. Rev. A 96 013817
[11] Rams M M, Sierant P, Dutta O, Horodecki P and Zakrzewski J 2018 Phys. Rev. X 8 021022
[12] Heugel T L, Biondi M, Zilberberg O and Chitra R 2019 Phys. Rev. Lett. 123 173601
[13] Garbe L, Bina M, Keller A, Paris M G A and Felicetti S 2020 Phys. Rev. Lett. 124 120504
[14] Lacroix C, Mendels P and Mila F 2011 Introduction to Frustrated Magnetism (Berlin: Springer)
[15] Balents L 2010 Nature 464 199
[16] Marić V, Giampaolo S M and Franchini F 2022 Phys. Rev. B 105 064408
[17] Ghosh S, Singh R R P and Kumar M 2025 Phys. Rev. B 111 045115
[18] Nersesyan A A, Gogolin A O and Ebßler F H L 1998 Phys. Rev. Lett. 81 910
[19] Mikeska H J and Luckmann C 2008 Phys. Rev. B 77 054405
[20] Derzhko O, Krokhmalskii T and Richter J 2010 Phys. Rev. B 82 214412
[21] Furuya S C and Giamarchi T 2014 Phys. Rev. B 89 205131
[22] Maiti D, Dey D and Kumar M 2018 J. Mag. Mag. Mater. 446 170
[23] Kolezhuk A K, Mikeska H J and Yamamoto S 1997 Phys. Rev. B 55 R3336
[24] Ivanov N B 2009 Condens. Matter Phys. 12 435
[25] Chandra V R, Ivanov N B and Richter J 2010 Phys. Rev. B 81 024409
[26] Jiang J J, Liu Y J, Tang F and Yang C H 2012 Phys. B 407 4810
[27] White S R 1992 Phys. Rev. Lett. 69 2863
[28] White S R 1998 Phys. Rep. 301 187
[29] Vidal G 2007 Phys. Rev. Lett. 98 070201
[30] Orus R and Vidal G 2008 Phys. Rev. B 78 155117
[31] Chen S, Wang Y, Ning W Q, Wu C and Lin H Q 2006 Phys. Rev. B 74 174424
[32] Cen L X 2022 arXiv:2208.03436v1 [cond-mat.str-el]
[33] Cen L X 2009 Phys. Rev. B 80 132405
[34] Pollmann F and Turner A M 2012 Phys. Rev. B 86 125441
[35] Pollmann F, Turner A M, Berg E and Oshikawa M 2018 Phys. Rev. B 81 064439
[36] Chen X, Gu Z C and Wen X G 2011 Phys. Rev. B 83 035107
[37] Schuch N, Pérez-García D and Cirac I 2011 Phys. Rev. B 84 165139
[38] Chen X, Gu Z C and Wen X G 2011 Phys. Rev. B 84 235128
[39] Jordan J, Orus R, Vidal G, Verstraete F and Cirac J 2008 Phys. Rev. B 101 250602
[40] Jiang H C, Weng Z Y and Xiang T 2008 Phys. Rev. Lett. 101 090603
[41] Cen L X 2018 Ann. Phys. 397 151
[42] Suzuki M 1990 Phys. Lett. A 146 319
[43] den Nijs M and Rommelse K 1989 Phys. Rev. B 40 4709
[44] Affleck I, Kennedy T, Lieb E H and Tasaki H 1987 Phys. Rev. Lett. 59 799
[45] Kennedy T and Tasaki H 1992 Phys. Rev. B 45 304
[46] Hida K 1992 Phys. Rev. B 45 2207
[47] Greiter M, Rachel S and Schuricht D 2007 Phys. Rev. B 75 060401
[48] Gong S S and Su G 2008 Phys. Rev. B 78 104416
[49] Perez-Garcia D, Wolf M M, Sanz M, Verstraete F and Cirac J I 2008 Phys. Rev. Lett. 100 167202
[50] Fu C, Zhao H, Chen Y G and Yan Y H 2021 Chin. Phys. B 30 087501
[51] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[52] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
