Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Quantum criticality with emergent symmetry in the extended Shastry-Sutherland model (2309.10955v2)

Published 19 Sep 2023 in cond-mat.str-el, cond-mat.mtrl-sci, and hep-th

Abstract: Motivated by the novel phenomena observed in the layered material $\rm SrCu_2(BO_3)_2$, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for $\rm SrCu_2(BO_3)_2$. However, the nature of its quantum phase transition from the plaquette valence-bond solid (PVBS) to antiferromagnetic (AFM) phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to $20 \times 20$ sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the PVBS and AFM phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of $\rm SrCu_2(BO_3)_2$.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (61)
  1. T. Senthil, Ashvin Vishwanath, Leon Balents, Subir Sachdev,  and Matthew P. A. Fisher, “Deconfined quantum critical points,” Science 303, 1490–1494 (2004a).
  2. T. Senthil, Leon Balents, Subir Sachdev, Ashvin Vishwanath,  and Matthew P. A. Fisher, “Quantum criticality beyond the landau-ginzburg-wilson paradigm,” Phys. Rev. B 70, 144407 (2004b).
  3. Anders W. Sandvik, “Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions,” Phys. Rev. Lett. 98, 227202 (2007).
  4. Roger G. Melko and Ribhu K. Kaul, “Scaling in the fan of an unconventional quantum critical point,” Phys. Rev. Lett. 100, 017203 (2008).
  5. F-J Jiang, M Nyfeler, S Chandrasekharan,  and U-J Wiese, “From an antiferromagnet to a valence bond solid: evidence for a first-order phase transition,” Journal of Statistical Mechanics: Theory and Experiment 2008, P02009 (2008).
  6. Jie Lou, Anders W. Sandvik,  and Naoki Kawashima, “Antiferromagnetic to valence-bond-solid transitions in two-dimensional SU⁢(N)SU𝑁\text{SU}({N})SU ( italic_N ) Heisenberg models with multispin interactions,” Phys. Rev. B 80, 180414 (2009).
  7. Adam Nahum, P. Serna, J. T. Chalker, M. Ortuño,  and A. M. Somoza, “Emergent SO(5) symmetry at the néel to valence-bond-solid transition,” Phys. Rev. Lett. 115, 267203 (2015a).
  8. D. Charrier and F. Alet, “Phase diagram of an extended classical dimer model,” Phys. Rev. B 82, 014429 (2010).
  9. Anders W. Sandvik, “Continuous quantum phase transition between an antiferromagnet and a valence-bond solid in two dimensions: Evidence for logarithmic corrections to scaling,” Phys. Rev. Lett. 104, 177201 (2010a).
  10. Ribhu K. Kaul, “Quantum criticality in SU(3) and SU(4) antiferromagnets,” Phys. Rev. B 84, 054407 (2011).
  11. Matthew S. Block, Roger G. Melko,  and Ribhu K. Kaul, “Fate of ℂ⁢ℙN−1ℂsuperscriptℙ𝑁1\mathbb{CP}^{N-1}blackboard_C blackboard_P start_POSTSUPERSCRIPT italic_N - 1 end_POSTSUPERSCRIPT fixed points with q𝑞qitalic_q monopoles,” Phys. Rev. Lett. 111, 137202 (2013).
  12. Kenji Harada, Takafumi Suzuki, Tsuyoshi Okubo, Haruhiko Matsuo, Jie Lou, Hiroshi Watanabe, Synge Todo,  and Naoki Kawashima, “Possibility of deconfined criticality in su(n𝑛nitalic_n) heisenberg models at small n𝑛nitalic_n,” Phys. Rev. B 88, 220408 (2013).
  13. Kun Chen, Yuan Huang, Youjin Deng, A. B. Kuklov, N. V. Prokof’ev,  and B. V. Svistunov, “Deconfined criticality flow in the heisenberg model with ring-exchange interactions,” Phys. Rev. Lett. 110, 185701 (2013).
  14. Sumiran Pujari, Fabien Alet,  and Kedar Damle, “Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet,” Phys. Rev. B 91, 104411 (2015).
  15. Adam Nahum, J. T. Chalker, P. Serna, M. Ortuño,  and A. M. Somoza, “Deconfined quantum criticality, scaling violations, and classical loop models,” Phys. Rev. X 5, 041048 (2015b).
  16. Hui Shao, Wenan Guo,  and Anders W. Sandvik, “Quantum criticality with two length scales,” Science 352, 213–216 (2016).
  17. G. J. Sreejith, Stephen Powell,  and Adam Nahum, “Emergent SO(5) symmetry at the columnar ordering transition in the classical cubic dimer model,” Phys. Rev. Lett. 122, 080601 (2019).
  18. F. F. Assaad and Tarun Grover, “Simple fermionic model of deconfined phases and phase transitions,” Phys. Rev. X 6, 041049 (2016).
  19. Toshihiro Sato, Martin Hohenadler,  and Fakher F. Assaad, “Dirac fermions with competing orders: Non-Landau transition with emergent symmetry,” Phys. Rev. Lett. 119, 197203 (2017).
  20. Yi-Zhuang You, Yin-Chen He, Cenke Xu,  and Ashvin Vishwanath, “Symmetric fermion mass generation as deconfined quantum criticality,” Phys. Rev. X 8, 011026 (2018).
  21. Xue-Feng Zhang, Yin-Chen He, Sebastian Eggert, Roderich Moessner,  and Frank Pollmann, “Continuous easy-plane deconfined phase transition on the kagome lattice,” Phys. Rev. Lett. 120, 115702 (2018).
  22. Wen-Yuan Liu, Shou-Shu Gong, Yu-Bin Li, Didier Poilblanc, Wei-Qiang Chen,  and Zheng-Cheng Gu, “Gapless quantum spin liquid and global phase diagram of the spin-1/2 J1−J2subscript𝐽1subscript𝐽2{J}_{1}-{J}_{2}italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT square antiferromagnetic Heisenberg model,” Science Bulletin 67, 1034–1041 (2022a).
  23. Wen-Yuan Liu, Juraj Hasik, Shou-Shu Gong, Didier Poilblanc, Wei-Qiang Chen,  and Zheng-Cheng Gu, “Emergence of gapless quantum spin liquid from deconfined quantum critical point,” Phys. Rev. X 12, 031039 (2022b).
  24. Wen-Yuan Liu, Shou-Shu Gong, Wei-Qiang Chen,  and Zheng-Cheng Gu, “Emergent symmetry in quantum phase transition: From deconfined quantum critical point to gapless quantum spin liquid,” arXiv:2212.00707  (2022c).
  25. M. E. Zayed, Ch. Rüegg, A. M. Läuchli, C. Panagopoulos, S. S. Saxena, M. Ellerby, D. F. McMorrow, Th. Strässle, S. Klotz, G. Hamel, et al., “4-spin plaquette singlet state in the Shastry–Sutherland compound SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Nat. Phys. 13, 962–966 (2017).
  26. Jing Guo, Guangyu Sun, Bowen Zhao, Ling Wang, Wenshan Hong, Vladimir A. Sidorov, Nvsen Ma, Qi Wu, Shiliang Li, Zi Yang Meng, Anders W. Sandvik,  and Liling Sun, “Quantum phases of SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT from high-pressure thermodynamics,” Phys. Rev. Lett. 124, 206602 (2020).
  27. Yi Cui, Lu Liu, Huihang Lin, Kai-Hsin Wu, Wenshan Hong, Xuefei Liu, Cong Li, Ze Hu, Ning Xi, Shiliang Li, Rong Yu, Anders W. Sandvik,  and Weiqiang Yu, “Proximate deconfined quantum critical point in SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Science 380, 1179–1184 (2023).
  28. B. Sriram Shastry and Bill Sutherland, “Exact ground state of a quantum mechanical antiferromagnet,” Physica B+C 108, 1069–1070 (1981).
  29. Shin Miyahara and Kazuo Ueda, “Exact dimer ground state of the two dimensional heisenberg spin system SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Phys. Rev. Lett. 82, 3701–3704 (1999).
  30. Philippe Corboz and Frédéric Mila, “Tensor network study of the Shastry-Sutherland model in zero magnetic field,” Phys. Rev. B 87, 115144 (2013).
  31. C. Boos, S. P. G. Crone, I. A. Niesen, P. Corboz, K. P. Schmidt,  and F. Mila, “Competition between intermediate plaquette phases in SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT under pressure,” Phys. Rev. B 100, 140413 (2019).
  32. Jong Yeon Lee, Yi-Zhuang You, Subir Sachdev,  and Ashvin Vishwanath, “Signatures of a deconfined phase transition on the Shastry-Sutherland lattice: Applications to quantum critical SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Phys. Rev. X 9, 041037 (2019).
  33. Tokuro Shimokawa, “Signatures of finite-temperature mirror symmetry breaking in the S=12𝑆12{S}{=}{\frac{1}{2}}italic_S = divide start_ARG 1 end_ARG start_ARG 2 end_ARG Shastry-Sutherland model,” Phys. Rev. B 103, 134419 (2021).
  34. Ning Xi, Hongyu Chen, ZY Xie,  and Rong Yu, “First-order transition between the plaquette valence bond solid and antiferromagnetic phases of the Shastry-Sutherland model,” arXiv:2111.07368  (2021).
  35. Ahmet Keleş and Erhai Zhao, “Rise and fall of plaquette order in the Shastry-Sutherland magnet revealed by pseudofermion functional renormalization group,” Phys. Rev. B 105, L041115 (2022).
  36. Jianwei Yang, Anders W. Sandvik,  and Ling Wang, “Quantum criticality and spin liquid phase in the Shastry-Sutherland model,” Phys. Rev. B 105, L060409 (2022).
  37. Ling Wang, Yalei Zhang,  and Anders W Sandvik, “Quantum spin liquid phase in the Shastry-Sutherland model detected by an improved level spectroscopic method,” Chinese Physics Letters 39, 077502 (2022).
  38. Junsen Wang, Han Li, Ning Xi, Yuan Gao, Qing-Bo Yan, Wei Li,  and Gang Su, “Plaquette singlet transition, magnetic barocaloric effect, and spin supersolidity in the Shastry-Sutherland model,” arXiv:2302.06596  (2023).
  39. Zhenzhong Shi, Sachith Dissanayake, Philippe Corboz, William Steinhardt, David Graf, DM Silevitch, Hanna A Dabkowska, TF Rosenbaum, Frédéric Mila,  and Sara Haravifard, “Discovery of quantum phases in the Shastry-Sutherland compound SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT under extreme conditions of field and pressure,” Nature Communications 13, 2301 (2022).
  40. J Larrea Jiménez, SPG Crone, Ellen Fogh, Mohamed Ezzat Zayed, Rolf Lortz, Ekaterina Pomjakushina, Kaziemerzh Conder, Andreas M Läuchli, Lukas Weber, Stefan Wessel, et al., “A quantum magnetic analogue to the critical point of water,” Nature 592, 370–375 (2021).
  41. Akihisa Koga and Norio Kawakami, ‘‘Quantum phase transitions in the Shastry-Sutherland model for SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Phys. Rev. Lett. 84, 4461–4464 (2000).
  42. Yoshihiro Takushima, Akihisa Koga,  and Norio Kawakami, “Competing spin-gap phases in a frustrated quantum spin system in two dimensions,” Journal of the Physical Society of Japan 70, 1369–1374 (2001).
  43. Oleg A. Starykh, Akira Furusaki,  and Leon Balents, “Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet,” Phys. Rev. B 72, 094416 (2005).
  44. R. F. Bishop, P. H. Y. Li, D. J. J. Farnell, J. Richter,  and C. E. Campbell, “Frustrated heisenberg antiferromagnet on the checkerboard lattice: J1subscript𝐽1{J}_{1}italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT-J2subscript𝐽2{J}_{2}italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT model,” Phys. Rev. B 85, 205122 (2012).
  45. Haiyuan Zou, Fan Yang,  and Wei Ku, “Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation,” arXiv:2011.06520  (2020).
  46. Wen-Yuan Liu, Shao-Jun Dong, Yong-Jian Han, Guang-Can Guo,  and Lixin He, “Gradient optimization of finite projected entangled pair states,” Phys. Rev. B 95, 195154 (2017).
  47. Wen-Yuan Liu, Shaojun Dong, Chao Wang, Yongjian Han, Hong An, Guang-Can Guo,  and Lixin He, “Gapless spin liquid ground state of the spin-1/2 J1subscript𝐽1{J}_{1}italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT-J2subscript𝐽2{J}_{2}italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT Heisenberg model on square lattices,” Phys. Rev. B 98, 241109 (2018).
  48. Wen-Yuan Liu, Yi-Zhen Huang, Shou-Shu Gong,  and Zheng-Cheng Gu, “Accurate simulation for finite projected entangled pair states in two dimensions,” Phys. Rev. B 103, 235155 (2021).
  49. Bowen Zhao, Phillip Weinberg,  and Anders W Sandvik, “Symmetry-enhanced discontinuous phase transition in a two-dimensional quantum magnet,” Nature Physics 15, 678–682 (2019).
  50. Pablo Serna and Adam Nahum, “Emergence and spontaneous breaking of approximate O⁢(4)O4\mathrm{O}(4)roman_O ( 4 ) symmetry at a weakly first-order deconfined phase transition,” Phys. Rev. B 99, 195110 (2019).
  51. Anders W. Sandvik, “Computational studies of quantum spin systems,” AIP Conference Proceedings 1297, 135–338 (2010b).
  52. Philippe Corboz, Piotr Czarnik, Geert Kapteijns,  and Luca Tagliacozzo, “Finite correlation length scaling with infinite projected entangled-pair states,” Phys. Rev. X 8, 031031 (2018).
  53. Michael Rader and Andreas M. Läuchli, ‘‘Finite correlation length scaling in Lorentz-invariant gapless iPEPS wave functions,” Phys. Rev. X 8, 031030 (2018).
  54. Bram Vanhecke, Juraj Hasik, Frank Verstraete,  and Laurens Vanderstraeten, “Scaling hypothesis for projected entangled-pair states,” Phys. Rev. Lett. 129, 200601 (2022).
  55. H. J. Liao, Z. Y. Xie, J. Chen, Z. Y. Liu, H. D. Xie, R. Z. Huang, B. Normand,  and T. Xiang, “Gapless spin-liquid ground state in the S=1/2𝑆12{S=1/2}italic_S = 1 / 2 kagome antiferromagnet,” Phys. Rev. Lett. 118, 137202 (2017).
  56. Hiroyuki Nojiri, Hiroshi Kageyama, Kenzo Onizuka, Yutaka Ueda,  and Mitsuhiro Motokawa, “Direct observation of the multiple spin gap excitations in two-dimensional dimer system SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Journal of the Physical Society of Japan 68, 2906–2909 (1999).
  57. Zhenzhong Shi, William Steinhardt, David Graf, Philippe Corboz, Franziska Weickert, Neil Harrison, Marcelo Jaime, Casey Marjerrison, Hanna A Dabkowska, Frédéric Mila, et al., “Emergent bound states and impurity pairs in chemically doped Shastry-Sutherland system,” Nature Communications 10, 2439 (2019).
  58. T Nomura, P Corboz, A Miyata, S Zherlitsyn, Y Ishii, Y Kohama, YH Matsuda, A Ikeda, C Zhong, H Kageyama, et al., “Unveiling new quantum phases in the Shastry-Sutherland compound SrCu2⁢(BO3)2subscriptSrCu2subscriptsubscriptBO32{{\rm SrCu_{2}(BO_{3})_{2}}}roman_SrCu start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( roman_BO start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT up to the saturation magnetic field,” Nature Communications 14, 3769 (2023).
  59. J. Ignacio Cirac, David Pérez-García, Norbert Schuch,  and Frank Verstraete, “Matrix product states and projected entangled pair states: Concepts, symmetries, theorems,” Rev. Mod. Phys. 93, 045003 (2021).
  60. Anders W. Sandvik, “Finite-size scaling and boundary effects in two-dimensional valence-bond solids,” Phys. Rev. B 85, 134407 (2012).
  61. Tom Vieijra, Jutho Haegeman, Frank Verstraete,  and Laurens Vanderstraeten, “Direct sampling of projected entangled-pair states,” Phys. Rev. B 104, 235141 (2021).
Citations (4)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now