|
|
|
Pattern description of quantum phase transitions in the transverse antiferromagnetic Ising model with a longitudinal field |
| Yun-Tong Yang(杨贇彤)1,2, Fu-Zhou Chen(陈富州)1,2, and Hong-Gang Luo(罗洪刚)1,2,† |
1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
2 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China |
|
|
|
|
Abstract A uniform longitudinal field applied to the transverse Ising model (TIM) distinguishes the antiferromagnetic Ising interaction from its ferromagnetic counterpart. While the ground state of the latter shows no quantum phase transition (QPT), the ground state of the former exhibits rich phases: paramagnetic, antiferromagnetic, and possibly disordered phases. Although the first two are clearly identified, the existence of the disordered phase remains controversial. Here, we use the pattern picture to explore the competition among the antiferromagnetic Ising interaction $J$, the transverse field $h_x$ and the longitudinal field $h_z$, and uncover which patterns are responsible for these three competing energy scales, thereby determining the possible phases and the QPTs among them. The system size ranges from $L=8$ to $128$ and the transverse field $h_x$ is fixed at $1$. Under these parameters, our results show the existence of the disordered phase. For a small $h_z$, the system transitions from a disordered phase to an antiferromagnetic phase as $J$ increases. For a large $h_z$, the system undergoes two phase transitions: from paramagnetic to disordered, and then to antiferromagnetic phase. These results not only unveil the rich physics of this paradigmatic model but also stimulate quantum simulation by using currently available experimental platforms.
|
Received: 04 July 2025
Revised: 04 September 2025
Accepted manuscript online: 21 October 2025
|
|
PACS:
|
75.10.Pq
|
(Spin chain models)
|
| |
75.40.Mg
|
(Numerical simulation studies)
|
| |
68.35.Rh
|
(Phase transitions and critical phenomena)
|
|
| Fund: The work is partly supported by the National Key Research and Development Program of China (Grant No. 2022YFA1402704) and the National Natural Science Foundation of China (Grant No. 12247101). |
Corresponding Authors:
Hong-Gang Luo
E-mail: luohg@lzu.edu.cn
|
| About author: 2025-127504-251151.pdf |
Cite this article:
Yun-Tong Yang(杨贇彤), Fu-Zhou Chen(陈富州), and Hong-Gang Luo(罗洪刚) Pattern description of quantum phase transitions in the transverse antiferromagnetic Ising model with a longitudinal field 2025 Chin. Phys. B 34 127504
|
[1] Lenz W 1920 Physikalische Zeitschrift 21 613
[2] Ising E 1925 Zeitschrift für Physik 31 253
[3] Niss M 2005 Archive for History of Exact Sciences 59 267
[4] Stanley H E 1987 Introduction to Phase Transitions and Critical Phenomena (Oxford: Oxford University Press)
[5] Kondepudi D and Prigogine I 1998 Modern Thermodynamics-From Heat Engines to Dissipative Systems (Chichester: Wiley)
[6] Chaikin P M and Lubensky T C 2000 Principles of Condensed Matter Physics (Cambridge University Press)
[7] Sachdev S 2011 Quantum phase transitions 2nd Edn. (Cambridge: Cambridge University Press)
[8] Suzuki S, ichi Inoue J and Chakrabarti B K 2013 Quantum Ising Phases and Transitions in Transverse Ising Models (ADS)
[9] Dutta A, Aeppli G, Chakrabarti B K, Divakaran U, Rosenbaum T F and Sen D 2015 Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information (Cambridge University Press)
[10] Friedenauer A, Schmitz H, Glueckert J T, Porras D and Schaetz T 2008 Nat. Phys. 4 757
[11] Simon J, Bakr W S, Ma R, Tai M E, Preiss P M and Greiner M 2011 Nature 472 307
[12] Islam R, Edwards E, Kim K, Korenblit S, Noh C, Carmichael H, Lin G D, Duan L M, Joseph Wang C C, Freericks J and Monroe C 2011 Nat. Commun. 2 377
[13] Kim K, Korenblit S, Islam R, Edwards E E, Chang M S, Noh C, Carmichael H, Lin G D, Duan L M, Wang C C J, Freericks J K and Monroe C 2011 New J. Phys. 13 105003
[14] Lewenstein M, Sanpera A and Ahufinger V 2012 Ultracold Atoms in Optical Lattices: Simulating Quantum Many-body Systems (Oxford: Oxford University Press)
[15] Georgescu I M, Ashhab S and Nori F 2014 Rev. Mod. Phys. 86 153
[16] Monroe C, CampbellWC, Duan L M, Gong Z X, Gorshkov A V, Hess PW, Islam R, Kim K, Linke N M, Pagano G, Richerme P, Senko C and Yao N Y 2021 Rev. Mod. Phys. 93 025001
[17] Scholl P, Schuler M, Williams H J, Eberharter A A, Barredo D, Schymik K N, Lienhard V, Henry L P, Lang T C, Lahaye T, Laeuchli A M and Browaeys A 2021 Nature 595 233
[18] Kadowaki T and Nishimori H 1998 Phys. Rev. E 58 5355
[19] Das A and Chakrabarti B K 2008 Rev. Mod. Phys. 80 1061
[20] Johnson M W, Amin M H S, Gildert S, Lanting T, Hamze F, Dickson N, Harris R, Berkley A J, Johansson J, Bunyk P, Chapple E M, Enderud C, Hilton J P, Karimi K, Ladizinsky E, Ladizinsky N, Oh T, Perminov I, Rich C, Thom M C, Tolkacheva E, Truncik C J S, Uchaikin S, Wang J, Wilson B and Rose G 2011 Nature 473 194
[21] Graß T 2019 Phys. Rev. Lett. 123 120501
[22] Onsager L 1944 Phys. Rev. 65 117
[23] Wilson K G 1975 Rev. Mod. Phys. 47 773
[24] Pfeuty P 1970 Annals of Physics 57 79
[25] Sen P 2000 Phys. Rev. E 63 016112
[26] Ovchinnikov A A, Dmitriev D V, Krivnov V Y and Cheranovskii V O 2003 Phys. Rev. B 68 214406
[27] Lajkó P, d’Auriac J C A, Rieger H and Iglói F 2020 Phys. Rev. B 101 024203
[28] Lajkó P and Iglói F 2021 Phys. Rev. B 103 174404
[29] Lin Y P, Kao Y J, Chen P and Lin Y C 2017 Phys. Rev. B 96 064427
[30] Bonfim O F d A, Boechat B and Florencio J 2019 Phys. Rev. E 99 012122
[31] Thouless D J 1969 Phys. Rev. 187 732
[32] Anderson P W and Yuval G 1969 Phys. Rev. Lett. 23 89
[33] Bar A and Mukamel D 2014 Phys. Rev. Lett. 112 015701
[34] Sheinman M, Sharma A, Alvarado J, Koenderink G H and MacKintosh F C 2015 Phys. Rev. Lett. 114 098104
[35] Alert R, Tierno P and Casademunt J 2017 Proc. Natl. Acad. Sci. USA 114 12906
[36] Gross B, Bonamassa I and Havlin S 2022 Phys. Rev. Lett. 129 268301
[37] Yang Y T, Chen F Z and Luo H G 2025 Phys. Rev. E 112 044102
[38] Yang Y T, Chen F Z and Luo H G arXiv: 2301.08891
[39] Bernien H, Schwartz S, Keesling A, Levine H, Omran A, Pichler H, Choi S, Zibrov A S, Endres M, Greiner M, Vuletic V and Lukin M D 2017 Nature 551 579
[40] Keesling A, Omran A, Levine H, Bernien H, Pichler H, Choi S, Samajdar R, Schwartz S, Silvi P, Sachdev S, Zoller P, Endres M, Greiner M, Vuletić V and Lukin M D 2019 Nature 568 207 |
| 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
|
|
|
