Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
149 tokens/sec
GPT-4o
9 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-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations (2403.05223v2)

Published 8 Mar 2024 in cond-mat.str-el, cond-mat.stat-mech, and quant-ph

Abstract: We study the ferromagnetic transverse-field Ising model with quenched disorder at $T = 0$ in one and two dimensions by means of stochastic series expansion quantum Monte Carlo simulations using a rigorous zero-temperature scheme. Using a sample-replication method and averaged Binder ratios, we determine the critical shift and width exponents $\nu_\mathrm{s}$ and $\nu_\mathrm{w}$ as well as unbiased critical points by finite-size scaling. Further, scaling of the disorder-averaged magnetisation at the critical point is used to determine the order-parameter critical exponent $\beta$ and the critical exponent $\nu_{\mathrm{av}}$ of the average correlation length. The dynamic scaling in the Griffiths phase is investigated by measuring the local susceptibility in the disordered phase and the dynamic exponent $z'$ is extracted. By applying various finite-size scaling protocols, we provide an extensive and comprehensive comparison between the different approaches on equal footing. The emphasis on effective zero-temperature simulations resolves several inconsistencies in existing literature.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (85)
  1. M. Vojta, Quantum phase transitions, Reports on Progress in Physics 66(12), 2069–2110 (2003), 10.1088/0034-4885/66/12/r01.
  2. S. Sachdev, Quantum Phase Transitions, Cambridge University Press, 2 edn., ISBN 9780511973765, 10.1017/CBO9780511973765 (2011).
  3. P. Pfeuty and R. J. Elliott, The Ising model with a transverse field. II. Ground state properties, Journal of Physics C: Solid State Physics 4(15), 2370 (1971), 10.1088/0022-3719/4/15/024.
  4. Two-dimensional periodic frustrated ising models in a transverse field, Phys. Rev. Lett. 84, 4457 (2000), 10.1103/PhysRevLett.84.4457.
  5. R. Moessner and S. L. Sondhi, Ising models of quantum frustration, Phys. Rev. B 63(22) (2001), 10.1103/PhysRevB.63.224401.
  6. S. V. Isakov and R. Moessner, Interplay of quantum and thermal fluctuations in a frustrated magnet, Phys. Rev. B 68, 104409 (2003), 10.1103/PhysRevB.68.104409.
  7. Disorder by disorder and flat bands in the kagome transverse field ising model, Phys. Rev. B 87, 054404 (2013), 10.1103/PhysRevB.87.054404.
  8. A. Dutta and J. K. Bhattacharjee, Phase transitions in the quantum ising and rotor models with a long-range interaction, Phys. Rev. B 64, 184106 (2001), 10.1103/PhysRevB.64.184106.
  9. N. Defenu, A. Trombettoni and S. Ruffo, Criticality and phase diagram of quantum long-range o(n𝑛nitalic_n) models, Phys. Rev. B 96, 104432 (2017), 10.1103/PhysRevB.96.104432.
  10. Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations, Phys. Rev. B 103, 245135 (2021), 10.1103/PhysRevB.103.245135.
  11. Scaling at quantum phase transitions above the upper critical dimension, SciPost Phys. 13, 088 (2022), 10.21468/SciPostPhys.13.4.088.
  12. Long-range interacting quantum systems, Rev. Mod. Phys. 95, 035002 (2023), 10.1103/RevModPhys.95.035002.
  13. Monte carlo based techniques for quantum magnets with long-range interactions (2024), 2403.00421.
  14. Quantum phases in circuit qed with a superconducting qubit array, Scientific Reports 4(1), 4083 (2014), 10.1038/srep04083.
  15. Ising model in a light-induced quantized transverse field, Phys. Rev. Res. 2, 023131 (2020), 10.1103/PhysRevResearch.2.023131.
  16. Direct observation and control of magnetic monopole defects in an artificial spin-ice material, New Journal of Physics 13(6), 063032 (2011), 10.1088/1367-2630/13/6/063032.
  17. Reducing disorder in artificial kagome ice, Phys. Rev. Lett. 107, 167201 (2011), 10.1103/PhysRevLett.107.167201.
  18. Non-fermi-liquid behavior within the ferromagnetic phase in uru2−x⁢rex⁢si2subscriptnormal-uru2𝑥subscriptnormal-re𝑥subscriptnormal-si2{\mathrm{u}\mathrm{r}\mathrm{u}}_{2-x}{\mathrm{r}\mathrm{e}}_{x}{\mathrm{s}% \mathrm{i}}_{2}roman_uru start_POSTSUBSCRIPT 2 - italic_x end_POSTSUBSCRIPT roman_re start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT roman_si start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, Physical Review Letters 94(4) (2005), 10.1103/physrevlett.94.046401.
  19. A. Schroeder, S. Ubaid-Kassis and T. Vojta, Signatures of a quantum griffiths phase in a d-metal alloy close to its ferromagnetic quantum critical point, Journal of Physics: Condensed Matter 23(9), 094205 (2011), 10.1088/0953-8984/23/9/094205.
  20. Dynamics of a bond-disordered s=1𝑠1s=1italic_s = 1 quantum magnet near z=1𝑧1z=1italic_z = 1 criticality, Phys. Rev. B 92, 024429 (2015), 10.1103/PhysRevB.92.024429.
  21. Metallic quantum ferromagnets, Rev. Mod. Phys. 88, 025006 (2016), 10.1103/RevModPhys.88.025006.
  22. Order by quenched disorder in the model triangular antiferromagnet RbFe⁢(moo4)2normal-RbFesubscriptsubscriptnormal-moo42\mathrm{RbFe}({\mathrm{moo}}_{4}{)}_{2}roman_RbFe ( roman_moo start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, Phys. Rev. Lett. 119, 047204 (2017), 10.1103/PhysRevLett.119.047204.
  23. Spin waves near the edge of halogen substitution induced magnetic order in ni⁢(cl1−x⁢brx)2⋅4⁢S⁢C⁢(NH2)2normal-⋅normal-nisubscriptsubscriptnormal-cl1𝑥subscriptnormal-br𝑥24normal-Snormal-Csubscriptsubscriptnormal-NH22{\mathrm{ni}(\mathrm{cl}}_{1-x}{\mathrm{br}}_{x}{{)}_{2}\cdot{}4{\mathrm{SC}(% \mathrm{NH}}_{2})}_{2}roman_ni ( roman_cl start_POSTSUBSCRIPT 1 - italic_x end_POSTSUBSCRIPT roman_br start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ⋅ 4 roman_S roman_C ( roman_NH start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, Phys. Rev. B 98, 214419 (2018), 10.1103/PhysRevB.98.214419.
  24. T. Vojta and J. A. Hoyos, Criticality and quenched disorder: Harris criterion versus rare regions, Phys. Rev. Lett. 112, 075702 (2014), 10.1103/PhysRevLett.112.075702.
  25. R. B. Griffiths, Nonanalytic behavior above the critical point in a random ising ferromagnet, Phys. Rev. Lett. 23, 17 (1969), 10.1103/PhysRevLett.23.17.
  26. B. M. McCoy, Incompleteness of the critical exponent description for ferromagnetic systems containing random impurities, Phys. Rev. Lett. 23, 383 (1969), 10.1103/PhysRevLett.23.383.
  27. A. B. Harris, Effect of random defects on the critical behaviour of ising models, Journal of Physics C: Solid State Physics 7(9), 1671 (1974), 10.1088/0022-3719/7/9/009.
  28. D. S. Fisher, Random transverse field ising spin chains, Phys. Rev. Lett. 69, 534 (1992), 10.1103/PhysRevLett.69.534.
  29. D. S. Fisher, Critical behavior of random transverse-field ising spin chains, Phys. Rev. B 51, 6411 (1995), 10.1103/PhysRevB.51.6411.
  30. D. S. Fisher, Phase transitions and singularities in random quantum systems, Physica A: Statistical Mechanics and its Applications 263(1–4), 222–233 (1999), 10.1016/s0378-4371(98)00498-1.
  31. S.-k. Ma, C. Dasgupta and C.-k. Hu, Random antiferromagnetic chain, Phys. Rev. Lett. 43, 1434 (1979), 10.1103/PhysRevLett.43.1434.
  32. Infinite-randomness quantum ising critical fixed points, Phys. Rev. B 61, 1160 (2000), 10.1103/PhysRevB.61.1160.
  33. F. Igloi and C. Monthus, Strong disorder RG approach of random systems, Physics Reports 412(5-6), 277 (2005), 10.1016/j.physrep.2005.02.006.
  34. I. A. Kovács and F. Iglói, Critical behavior and entanglement of the random transverse-field ising model between one and two dimensions, Phys. Rev. B 80, 214416 (2009), 10.1103/PhysRevB.80.214416.
  35. I. A. Kovács and F. Iglói, Renormalization group study of the two-dimensional random transverse-field ising model, Phys. Rev. B 82, 054437 (2010), 10.1103/PhysRevB.82.054437.
  36. C. Monthus and T. Garel, The random transverse field ising model in d = 2: analysis via boundary strong disorder renormalization, Journal of Statistical Mechanics: Theory and Experiment 2012(09), P09016 (2012), 10.1088/1742-5468/2012/09/P09016.
  37. A. Crisanti and H. Rieger, Random-bond ising chain in a transverse magnetic field: A finite-size scaling analysis, Journal of Statistical Physics 77(5-6), 1087 (1994), 10.1007/bf02183154.
  38. H. Rieger and N. Kawashima, Application of a continuous time cluster algorithm to the two-dimensional random quantum ising ferromagnet, The European Physical Journal B - Condensed Matter and Complex Systems 9(2), 233 (1999), 10.1007/s100510050761.
  39. Critical behavior and griffiths-mccoy singularities in the two-dimensional random quantum ising ferromagnet, Phys. Rev. Lett. 81, 5916 (1998), 10.1103/PhysRevLett.81.5916.
  40. J. Choi and S. K. Baek, Finite-size scaling analysis of the two-dimensional random transverse-field ising ferromagnet, Phys. Rev. B 108, 144204 (2023), 10.1103/PhysRevB.108.144204.
  41. A. W. Sandvik and J. Kurkijärvi, Quantum monte carlo simulation method for spin systems, Phys. Rev. B 43, 5950 (1991), 10.1103/PhysRevB.43.5950.
  42. A. W. Sandvik, A generalization of handscombs quantum monte carlo scheme-application to the 1d hubbard model, Journal of Physics A: Mathematical and General 25(13), 3667 (1992), 10.1088/0305-4470/25/13/017.
  43. A. W. Sandvik, Stochastic series expansion method for quantum ising models with arbitrary interactions, Phys. Rev. E 68, 056701 (2003), 10.1103/PhysRevE.68.056701.
  44. Computational studies of quantum spin systems, In AIP Conference Proceedings. AIP, 10.1063/1.3518900 (2010).
  45. P. Pfeuty, The one-dimensional ising model with a transverse field, Annals of Physics 57(1), 79 (1970), https://doi.org/10.1016/0003-4916(70)90270-8.
  46. Ising model with a transverse field, Phys. Rev. Lett. 25, 443 (1970), 10.1103/PhysRevLett.25.443.
  47. P. Pfeuty, An exact result for the 1d random ising model in a transverse field, Physics Letters A 72(3), 245 (1979), https://doi.org/10.1016/0375-9601(79)90017-3.
  48. D. S. Fisher, Random antiferromagnetic quantum spin chains, Phys. Rev. B 50, 3799 (1994), 10.1103/PhysRevB.50.3799.
  49. F. Iglói and C. Monthus, Strong disorder RG approach – a short review of recent developments, The European Physical Journal B 91(11) (2018), 10.1140/epjb/e2018-90434-8.
  50. A. P. Young and H. Rieger, Numerical study of the random transverse-field ising spin chain, Phys. Rev. B 53, 8486 (1996), 10.1103/PhysRevB.53.8486.
  51. Finite-size scaling of pseudocritical point distributions in the random transverse-field ising chain, Phys. Rev. B 76, 064421 (2007), 10.1103/PhysRevB.76.064421.
  52. Numerical Renormalization Group Study of Random Transverse Ising Models in One and Two Space Dimensions, Progress of Theoretical Physics Supplement 138, 479 (2000), 10.1143/PTPS.138.479, https://academic.oup.com/ptps/article-pdf/doi/10.1143/PTPS.138.479/5313523/138-479.pdf.
  53. R. Yu, H. Saleur and S. Haas, Entanglement entropy in the two-dimensional random transverse field ising model, Phys. Rev. B 77, 140402 (2008), 10.1103/PhysRevB.77.140402.
  54. S. Humeniuk, Quantum Monte Carlo studies of strongly correlated systems for quantum simulators, Ph.D. thesis (2018).
  55. Equation of state calculations by fast computing machines, The Journal of Chemical Physics 21(6), 1087–1092 (1953), 10.1063/1.1699114.
  56. W. K. Hastings, Monte carlo sampling methods using markov chains and their applications, Biometrika 57(1), 97–109 (1970), 10.1093/biomet/57.1.97.
  57. A. W. Sandvik, Classical percolation transition in the diluted two-dimensional s=12𝑠12s=\frac{1}{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG heisenberg antiferromagnet, Phys. Rev. B 66, 024418 (2002), 10.1103/PhysRevB.66.024418.
  58. T. Vojta, Disorder in quantum many-body systems, Annual Review of Condensed Matter Physics 10(1), 233 (2019), 10.1146/annurev-conmatphys-031218-013433.
  59. I. Antonov and V. Saleev, An economic method of computing lpτ𝜏\tauitalic_τ-sequences, USSR Computational Mathematics and Mathematical Physics 19(1), 252–256 (1979), 10.1016/0041-5553(79)90085-5.
  60. P. Bratley and B. L. Fox, Algorithm 659: Implementing sobol’s quasirandom sequence generator, ACM Transactions on Mathematical Software 14(1), 88–100 (1988), 10.1145/42288.214372.
  61. Quasi-monte carlo integration, Journal of Computational Physics 122(2), 218–230 (1995), 10.1006/jcph.1995.1209.
  62. I. Sobol’, On the distribution of points in a cube and the approximate evaluation of integrals, USSR Computational Mathematics and Mathematical Physics 7(4), 86–112 (1967), 10.1016/0041-5553(67)90144-9.
  63. K. G. Wilson, Renormalization group and critical phenomena. i. renormalization group and the kadanoff scaling picture, Phys. Rev. B 4, 3174 (1971), 10.1103/PhysRevB.4.3174.
  64. K. G. Wilson, Renormalization group and critical phenomena. ii. phase-space cell analysis of critical behavior, Phys. Rev. B 4, 3184 (1971), 10.1103/PhysRevB.4.3184.
  65. A. Hankey and H. E. Stanley, Systematic application of generalized homogeneous functions to static scaling, dynamic scaling, and universality, Phys. Rev. B 6, 3515 (1972), 10.1103/PhysRevB.6.3515.
  66. E. Brézin, An investigation of finite size scaling, Journal de Physique 43(1), 15–22 (1982), 10.1051/jphys:0198200430101500.
  67. E. Brézin and J. Zinn-Justin, Finite size effects in phase transitions, Nuclear Physics B 257, 867–893 (1985), 10.1016/0550-3213(85)90379-7.
  68. K. Binder, Finite size effects on phase transitions, Ferroelectrics 73(1), 43 (1987), 10.1080/00150198708227908.
  69. T. R. Kirkpatrick and D. Belitz, Exponent relations at quantum phase transitions with applications to metallic quantum ferromagnets, Phys. Rev. B 91, 214407 (2015), 10.1103/PhysRevB.91.214407.
  70. Scaling theory for finite-size effects in the critical region, Phys. Rev. Lett. 28, 1516 (1972), 10.1103/PhysRevLett.28.1516.
  71. Griffiths singularities in the random quantum ising antiferromagnet: A tree tensor network renormalization group study, Phys. Rev. B 96, 064427 (2017), 10.1103/PhysRevB.96.064427.
  72. C. Śliwa, Disorder-averaged binder ratio in site-diluted heisenberg models (2022), 10.48550/ARXIV.2205.00977.
  73. Finite-size scaling in ising-like systems with quenched random fields: Evidence of hyperscaling violation, Phys. Rev. E 82, 051134 (2010), 10.1103/PhysRevE.82.051134.
  74. R. Sknepnek, T. Vojta and M. Vojta, Exotic versus conventional scaling and universality in a disordered bilayer quantum heisenberg antiferromagnet, Physical Review Letters 93(9) (2004), 10.1103/physrevlett.93.097201.
  75. K. S. D. Beach, L. Wang and A. W. Sandvik, Data collapse in the critical region using finite-size scaling with subleading corrections (2005), 10.48550/ARXIV.COND-MAT/0505194.
  76. Distribution of pseudo-critical temperatures and lack of self-averaging in disordered poland-scheraga models with different loop exponents, Eur. Phys. J. B 48(3), 393 (2005), 10.1140/epjb/e2005-00417-7.
  77. R. Miyazaki and H. Nishimori, Real-space renormalization-group approach to the random transverse-field ising model in finite dimensions, Phys. Rev. E 87, 032154 (2013), 10.1103/PhysRevE.87.032154.
  78. T. Vojta, A. Farquhar and J. Mast, Infinite-randomness critical point in the two-dimensional disordered contact process, Phys. Rev. E 79, 011111 (2009), 10.1103/PhysRevE.79.011111.
  79. S. Wiseman and E. Domany, Lack of self-averaging in critical disordered systems, Phys. Rev. E 52, 3469 (1995), 10.1103/PhysRevE.52.3469.
  80. Order as an effect of disorder, J. Phys. France 41(11), 1263 (1980), 10.1051/jphys:0198000410110126300.
  81. D. J. Priour, M. P. Gelfand and S. L. Sondhi, Disorder from disorder in a strongly frustrated transverse-field ising chain, Phys. Rev. B 64, 134424 (2001), 10.1103/PhysRevB.64.134424.
  82. H. Niederreiter, Quasi-monte carlo methods and pseudo-random numbers, Bulletin of the American Mathematical Society 84(6), 957–1041 (1978), 10.1090/s0002-9904-1978-14532-7.
  83. P. Jordan and E. Wigner, Über das paulische Äquivalenzverbot, Zeitschrift für Physik 47(9–10), 631–651 (1928), 10.1007/bf01331938.
  84. T. Matsubara and H. Matsuda, A lattice model of liquid helium, i, Progress of Theoretical Physics 16(6), 569–582 (1956), 10.1143/ptp.16.569.
  85. G. B. Mbeng, A. Russomanno and G. E. Santoro, The quantum ising chain for beginners (2020), 10.48550/ARXIV.2009.09208.
Citations (1)

Summary

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