Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 81 tok/s
Gemini 2.5 Pro 45 tok/s Pro
GPT-5 Medium 14 tok/s Pro
GPT-5 High 16 tok/s Pro
GPT-4o 86 tok/s Pro
Kimi K2 145 tok/s Pro
GPT OSS 120B 446 tok/s Pro
Claude Sonnet 4 37 tok/s Pro
2000 character limit reached

Entanglement-enabled symmetry-breaking orders (2207.08828v2)

Published 18 Jul 2022 in cond-mat.str-el, cond-mat.quant-gas, cond-mat.stat-mech, hep-th, and quant-ph

Abstract: A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (48)
  1. S.-S. Gong, W. Zhu and D. N. Sheng, Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model, Scientific Reports 4, 6317 (2014), 10.1038/srep06317, 1312.4519.
  2. Su(2n) quantum antiferromagnets with exact c-breaking ground states, Nuclear Physics B 366(3), 467 (1991), https://doi.org/10.1016/0550-3213(91)90027-U.
  3. N. Shannon, T. Momoi and P. Sindzingre, Nematic Order in Square Lattice Frustrated Ferromagnets, Phys. Rev. Lett. 96(2), 027213 (2006), 10.1103/PhysRevLett.96.027213, cond-mat/0512349.
  4. Where is the Quantum Spin Nematic?, Phys. Rev. Lett. 130(11), 116701 (2023), 10.1103/PhysRevLett.130.116701, 2209.00010.
  5. A. J. Beekman, L. Rademaker and J. van Wezel, An Introduction to Spontaneous Symmetry Breaking, SciPost Phys. Lect. Notes p. 11 (2019), 10.21468/SciPostPhysLectNotes.11.
  6. F. Lu and Y.-M. Lu, Magnon band topology in spin-orbital coupled magnets: classification and application to α𝛼\alphaitalic_α-RuCl33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT, arXiv e-prints arXiv:1807.05232 (2018), 1807.05232.
  7. Spin-space groups and magnon band topology, Phys. Rev. B 105(6), 064430 (2022), 10.1103/PhysRevB.105.064430, 2103.05656.
  8. Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling, Phys. Rev. X 12(2), 021016 (2022), 10.1103/PhysRevX.12.021016, 2103.15723.
  9. P. A. McClarty, Topological magnons: A review, Annual Review of Condensed Matter Physics 13(1), 171 (2022), 10.1146/annurev-conmatphys-031620-104715.
  10. An efficient material search for room-temperature topological magnons, Science Advances 9(7), eade7731 (2023), 10.1126/sciadv.ade7731.
  11. A. Fert, N. Reyren and V. Cros, Magnetic skyrmions: advances in physics and potential applications, Nature Reviews Materials 2(7), 17031 (2017), 10.1038/natrevmats.2017.31, 1712.07236.
  12. Y. Zhou, Magnetic skyrmions: intriguing physics and new spintronic device concepts, National Science Review 6(2), 210 (2018), 10.1093/nsr/nwy109.
  13. C. H. Marrows and K. Zeissler, Perspective on skyrmion spintronics, Applied Physics Letters 119(25), 250502 (2021), 10.1063/5.0072735.
  14. E. Lieb, T. Schultz and D. Mattis, Two soluble models of an antiferromagnetic chain, Annals of Physics 16(3), 407 (1961), https://doi.org/10.1016/0003-4916(61)90115-4.
  15. M. Oshikawa, Commensurability, Excitation Gap, and Topology in Quantum Many-Particle Systems on a Periodic Lattice, Phys. Rev. Lett. 84(7), 1535 (2000), 10.1103/PhysRevLett.84.1535, cond-mat/9911137.
  16. M. B. Hastings, Lieb-Schultz-Mattis in higher dimensions, Phys. Rev. B 69(10), 104431 (2004), 10.1103/PhysRevB.69.104431, cond-mat/0305505.
  17. Lattice Homotopy Constraints on Phases of Quantum Magnets, Phys. Rev. Lett. 119(12), 127202 (2017), 10.1103/PhysRevLett.119.127202, 1703.06882.
  18. Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases, SciPost Phys. 11, 24 (2021), 10.21468/SciPostPhys.11.2.024.
  19. Symmetry protection of topological phases in one-dimensional quantum spin systems, Phys. Rev. B 85(7), 075125 (2012), 10.1103/PhysRevB.85.075125, 0909.4059.
  20. Entanglement spectrum of a topological phase in one dimension, Phys. Rev. B 81(6), 064439 (2010), 10.1103/PhysRevB.81.064439, 0910.1811.
  21. X. Chen, Z.-C. Gu and X.-G. Wen, Classification of gapped symmetric phases in one-dimensional spin systems, Phys. Rev. B 83(3), 035107 (2011), 10.1103/PhysRevB.83.035107, 1008.3745.
  22. S. Jiang and Y. Ran, Anyon condensation and a generic tensor-network construction for symmetry-protected topological phases, Phys. Rev. B 95(12), 125107 (2017), 10.1103/PhysRevB.95.125107, 1611.07652.
  23. R. Thorngren and D. V. Else, Gauging spatial symmetries and the classification of topological crystalline phases, Phys. Rev. X 8, 011040 (2018), 10.1103/PhysRevX.8.011040.
  24. D. V. Else and R. Thorngren, Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems, Phys. Rev. B 101(22), 224437 (2020), 10.1103/PhysRevB.101.224437, 1907.08204.
  25. E. Majorana, Atomi orientati in campo magnetico variabile, Il Nuovo Cimento (1924-1942) 9(2), 43 (1932), 10.1007/BF02960953.
  26. F. Bloch and I. I. Rabi, Atoms in variable magnetic fields, Rev. Mod. Phys. 17, 237 (1945), 10.1103/RevModPhys.17.237.
  27. H. Mäkelä and A. Messina, N-qubit states as points on the Bloch sphere, Physica Scripta Volume T 140, 014054 (2010), 10.1088/0031-8949/2010/T140/014054, 0910.0630.
  28. Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface, Phys. Rev. X 6(4), 041068 (2016), 10.1103/PhysRevX.6.041068, 1511.02263.
  29. N. Papanicolaou, Unusual phases in quantum spin-1 systems, Nuclear Physics B 305(3), 367 (1988), https://doi.org/10.1016/0550-3213(88)90073-9.
  30. Valence bond ground states in isotropic quantum antiferromagnets, Communications in Mathematical Physics 115(3), 477 (1988), 10.1007/BF01218021.
  31. Featureless quantum insulator on the honeycomb lattice, Phys. Rev. B 94(6), 064432 (2016), 10.1103/PhysRevB.94.064432, 1509.04358.
  32. Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality, arXiv e-prints arXiv:2111.12097 (2021), 2111.12097.
  33. A. Keselman and E. Berg, Gapless symmetry-protected topological phase of fermions in one dimension, Phys. Rev. B 91(23), 235309 (2015), 10.1103/PhysRevB.91.235309, 1502.02037.
  34. Gapless Symmetry-Protected Topological Order, Phys. Rev. X 7(4), 041048 (2017), 10.1103/PhysRevX.7.041048, 1705.01557.
  35. L. Li, M. Oshikawa and Y. Zheng, Symmetry Protected Topological Criticality: Decorated Defect Construction, Signatures and Stability, arXiv e-prints arXiv:2204.03131 (2022), 2204.03131.
  36. Z. Ringel and D. L. Kovrizhin, Quantized gravitational responses, the sign problem, and quantum complexity, Sci. Adv. 3(9), e1701758 (2017), 10.1126/sciadv.1701758.
  37. A. Smith, O. Golan and Z. Ringel, Intrinsic sign problems in topological quantum field theories, Phys. Rev. Research 2(3), 033515 (2020), 10.1103/PhysRevResearch.2.033515, 2005.05343.
  38. Symmetry-protected sign problem and magic in quantum phases of matter, Quantum 5, 612 (2021), 10.22331/q-2021-12-28-612.
  39. Probing sign structure using measurement-induced entanglement, Quantum 7, 910 (2023), 10.22331/q-2023-02-02-910.
  40. Fragile Topology and Wannier Obstructions, Phys. Rev. Lett. 121(12), 126402 (2018), 10.1103/PhysRevLett.121.126402, 1709.06551.
  41. D. V. Else, H. C. Po and H. Watanabe, Fragile topological phases in interacting systems, Phys. Rev. B 99(12), 125122 (2019), 10.1103/PhysRevB.99.125122, 1809.02128.
  42. K. Latimer and C. Wang, Correlated fragile topology: A parton approach, Phys. Rev. B 103(4), 045128 (2021), 10.1103/PhysRevB.103.045128, 2007.15605.
  43. Y.-M. Lu, Lieb-Schultz-Mattis theorems for symmetry protected topological phases, arXiv e-prints arXiv:1705.04691 (2017), 1705.04691.
  44. Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders, Phys. Rev. X 11(3), 031043 (2021), 10.1103/PhysRevX.11.031043, 2101.07805.
  45. B. Nachtergaele, The spectral gap for some spin chains with discrete symmetry breaking, Communications in Mathematical Physics 175(3), 565 (1996), 10.1007/BF02099509.
  46. String Order and Symmetries in Quantum Spin Lattices, Phys. Rev. Lett. 100(16), 167202 (2008), 10.1103/PhysRevLett.100.167202, 0802.0447.
  47. Matrix product states: Symmetries and two-body Hamiltonians, Phys. Rev. A 79(4), 042308 (2009), 10.1103/PhysRevA.79.042308, 0901.2223.
  48. H. Watanabe and H. Murayama, Effective Lagrangian for Nonrelativistic Systems, Phys. Rev. X 4(3), 031057 (2014), 10.1103/PhysRevX.4.031057, 1402.7066.
Citations (1)
View on Semantic Scholar
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

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

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

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

List Streamline Icon: https://streamlinehq.com Explore 13 Community Prompts
Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

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

Authors (2)

  1. Cheng-Ju Lin
  2. Liujun Zou
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets