Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
194 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 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

Anomalies of Average Symmetries: Entanglement and Open Quantum Systems (2312.09074v1)

Published 14 Dec 2023 in cond-mat.str-el, cond-mat.stat-mech, hep-th, and quant-ph

Abstract: Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed states resulting from non-commuting average symmetries. We will focus on the cases where the commutation relations of the average symmetry generators are violated by nontrivial phases, and call such average symmetry anomalous. We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues, and present several lattice examples with average symmetries, including XY chain, Heisenberg chain, and deformed toric code models. In certain cases, the results can be further extended to reduced density matrices, leading to a new lower bound on the entanglement entropy. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (128)
  1. E. Witten, “Global Aspects of Current Algebra,” Nucl. Phys. B 223 (1983) 422–432.
  2. E. H. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Annals Phys. 16 (1961) 407–466.
  3. M. Oshikawa, “Topological approach to Luttinger’s theorem and the Fermi surface of a Kondo lattice,” Phys. Rev. Lett. 84 no. 15, (2000) 3370, arXiv:cond-mat/0002392.
  4. M. B. Hastings, “Lieb–Schultz–Mattis in higher dimensions,” Phys. Rev. B 69 (2004) 104431, arXiv:cond-mat/0305505.
  5. D. V. Else and R. Thorngren, “Topological theory of Lieb–Schultz–Mattis theorems in quantum spin systems,” Phys. Rev. B 101 no. 22, (2020) 224437, arXiv:1907.08204 [cond-mat.str-el].
  6. M. Cheng and N. Seiberg, “Lieb-Schultz-Mattis, Luttinger, and ’t Hooft - anomaly matching in lattice systems,” SciPost Phys. 15 no. 2, (2023) 051, arXiv:2211.12543 [cond-mat.str-el].
  7. H. Shimizu and K. Yonekura, “Anomaly constraints on deconfinement and chiral phase transition,” Phys. Rev. D 97 no. 10, (2018) 105011, arXiv:1706.06104 [hep-th].
  8. P.-S. Hsin and A. Turzillo, “Symmetry-enriched quantum spin liquids in (3 + 1)d𝑑ditalic_d,” JHEP 09 (2020) 022, arXiv:1904.11550 [cond-mat.str-el].
  9. Z. Komargodski, K. Ohmori, K. Roumpedakis, and S. Seifnashri, “Symmetries and strings of adjoint QCD22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT,” JHEP 03 (2021) 103, arXiv:2008.07567 [hep-th].
  10. X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, “Symmetry protected topological orders and the group cohomology of their symmetry group,” Phys. Rev. B 87 no. 15, (2013) 155114, arXiv:1106.4772 [cond-mat.str-el].
  11. D. V. Else and C. Nayak, “Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge,” Phys. Rev. B 90 no. 23, (2014) 235137, arXiv:1409.5436 [cond-mat.str-el].
  12. E. Witten, “Fermion Path Integrals And Topological Phases,” Rev. Mod. Phys. 88 no. 3, (2016) 035001, arXiv:1508.04715 [cond-mat.mes-hall].
  13. M. Barkeshli, Y.-A. Chen, P.-S. Hsin, and R. Kobayashi, “Higher-group symmetry in finite gauge theory and stabilizer codes,” arXiv:2211.11764 [cond-mat.str-el].
  14. M. Barkeshli, P.-S. Hsin, and R. Kobayashi, “Higher-group symmetry of (3+1)D fermionic ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT gauge theory: logical CCZ, CS, and T gates from higher symmetry,” arXiv:2311.05674 [cond-mat.str-el].
  15. F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, “Spectral theory of Liouvillians for dissipative phase transitions,” Phys. Rev. A 98 (Oct, 2018) 042118, arXiv:1804.11293 [quant-ph].
  16. R. Ma and C. Wang, “Average Symmetry-Protected Topological Phases,” Phys. Rev. X 13 no. 3, (2023) 031016, arXiv:2209.02723 [cond-mat.str-el].
  17. J.-H. Zhang, Y. Qi, and Z. Bi, “Strange Correlation Function for Average Symmetry-Protected Topological Phases,” arXiv:2210.17485 [cond-mat.str-el].
  18. R. Ma, J.-H. Zhang, Z. Bi, M. Cheng, and C. Wang, “Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic,” arXiv:2305.16399 [cond-mat.str-el].
  19. J. Y. Lee, Y.-Z. You, and C. Xu, “Symmetry protected topological phases under decoherence,” arXiv:2210.16323 [cond-mat.str-el].
  20. F. Grusdt, “Topological order of mixed states in correlated quantum many-body systems,” Phys. Rev. B 95 (Feb, 2017) 075106, arXiv:1609.02432 [quant-ph].
  21. S. Sachdev, “Bekenstein-Hawking Entropy and Strange Metals,” Phys. Rev. X 5 no. 4, (2015) 041025, arXiv:1506.05111 [hep-th].
  22. A. Kitaev, “2015 Breakthrough Prize Fundamental Physics Symposium.” https://www.youtube.com/watch?v=OQ9qN8j7EZI.
  23. A. Kitaev, “Hidden correlations in the Hawking radiation and thermal noise.” http://online.kitp.ucsb.edu/online/joint98/kitaev/.
  24. A. Kitaev, “A simple model of quantum holography.”. http://online.kitp.ucsb.edu/online/entangled15/kitaev and http://online.kitp.ucsb.edu/online/entangled15/kitaev2.
  25. J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D94 no. 10, (2016) 106002, arXiv:1604.07818 [hep-th].
  26. A. Kitaev and S. J. Suh, “The soft mode in the Sachdev–Ye–Kitaev model and its gravity dual,” JHEP 05 (2018) 183, arXiv:1711.08467 [hep-th].
  27. X.-L. Qi, Z. Shangnan, and Z. Yang, “Holevo information and ensemble theory of gravity,” JHEP 02 (2022) 056, arXiv:2111.05355 [hep-th].
  28. A. Antinucci, G. Galati, G. Rizi, and M. Serone, “Symmetries and topological operators, on average,” arXiv:2305.08911 [hep-th].
  29. K. Kawabata, R. Sohal, and S. Ryu, “Lieb–Schultz–Mattis Theorem in Open Quantum Systems,” arXiv:2305.16496 [cond-mat.stat-mech].
  30. N. Seiberg and S.-H. Shao, “Majorana chain and Ising model – (non-invertible) translations, anomalies, and emanant symmetries,” arXiv:2307.02534 [cond-mat.str-el].
  31. I. Schur, “Neue Begründung der Theorie der Gruppencharaktere,” Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (1905) 406–432.
  32. M. Levin and X.-G. Wen, “Detecting Topological Order in a Ground State Wave Function,” Phys. Rev. Lett. 96 (2006) 110405, arXiv:cond-mat/0510613.
  33. A. Kitaev and J. Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96 (2006) 110404, arXiv:hep-th/0510092.
  34. I. V. Protopopov, W. W. Ho, and D. A. Abanin, “Effect of su(2) symmetry on many-body localization and thermalization,” Phys. Rev. B 96 (Jul, 2017) 041122, arXiv:1612.01208 [cond-mat.dis-nn].
  35. A. C. Potter and R. Vasseur, “Symmetry constraints on many-body localization,” Phys. Rev. B 94 no. 22, (2016) 224206, arXiv:1605.03601 [cond-mat.dis-nn].
  36. I. C. Fulga, B. van Heck, J. M. Edge, and A. R. Akhmerov, “Statistical Topological Insulators,” Phys. Rev. B 89 no. 15, (2014) 155424, arXiv:1212.6191 [cond-mat.mes-hall].
  37. A. Milsted, L. Seabra, I. C. Fulga, C. W. J. Beenakker, and E. Cobanera, “Statistical translation invariance protects a topological insulator from interactions,” Phys. Rev. B 92 (Aug, 2015) 085139, arXiv:1504.07258 [cond-mat.mes-hall].
  38. Z. Ringel, Y. E. Kraus, and A. Stern, “Strong side of weak topological insulators,” Phys. Rev. B 86 (2012) 045102, arXiv:1105.4351 [cond-mat.mtrl-sci].
  39. R. S. K. Mong, J. H. Bardarson, and J. E. Moore, “Quantum transport and two-parameter scaling at the surface of a weak topological insulator,” Phys. Rev. Lett. 108 (Feb, 2012) 076804, arXiv:1109.3201 [cond-mat.mes-hall].
  40. Lecture Notes in Physics. Springer Berlin Heidelberg, 1983.
  41. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010.
  42. C. de Groot, A. Turzillo, and N. Schuch, “Symmetry Protected Topological Order in Open Quantum Systems,” Quantum 6 (2022) 856, arXiv:2112.04483 [quant-ph].
  43. G. Lindblad, “On the Generators of Quantum Dynamical Semigroups,” Commun. Math. Phys. 48 (1976) 119.
  44. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, “Completely Positive Dynamical Semigroups of N Level Systems,” J. Math. Phys. 17 (1976) 821.
  45. K. Kawabata, A. Kulkarni, J. Li, T. Numasawa, and S. Ryu, “Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos,” PRX Quantum 4 no. 3, (2023) 030328, arXiv:2212.00605 [cond-mat.mes-hall].
  46. S. Lieu, R. Belyansky, J. T. Young, R. Lundgren, V. V. Albert, and A. V. Gorshkov, “Symmetry Breaking and Error Correction in Open Quantum Systems,” Phys. Rev. Lett. 125 no. 24, (2020) 240405, arXiv:2008.02816 [quant-ph].
  47. J. Cornwell, “Chapter 4 - representations of groups principal ideas,” in Group Theory in Physics, J. Cornwell, ed., vol. 1 of Techniques of Physics, pp. 47–63. Academic Press, San Diego, 1997.
  48. S. C. Furuya and M. Oshikawa, “Symmetry Protection of Critical Phases and a Global Anomaly in 1+1111+11 + 1 Dimensions,” Phys. Rev. Lett. 118 no. 2, (2017) 021601, arXiv:1503.07292 [cond-mat.stat-mech].
  49. M. Cheng, M. Zaletel, M. Barkeshli, A. Vishwanath, and P. Bonderson, “Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface,” Phys. Rev. X 6 no. 4, (2016) 041068, arXiv:1511.02263 [cond-mat.str-el].
  50. G. Y. Cho, S. Ryu, and C.-T. Hsieh, “Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases,” Phys. Rev. B 96 no. 19, (2017) 195105, arXiv:1705.03892 [cond-mat.str-el].
  51. M. A. Metlitski and R. Thorngren, “Intrinsic and emergent anomalies at deconfined critical points,” Phys. Rev. B 98 no. 8, (2018) 085140, arXiv:1707.07686 [cond-mat.str-el].
  52. L. Gioia and C. Wang, “Nonzero Momentum Requires Long-Range Entanglement,” Phys. Rev. X 12 no. 3, (2022) 031007, arXiv:2112.06946 [cond-mat.str-el].
  53. A. Hulpke, “Using gap,”. https://www.math.colostate.edu/~hulpke/paper/gap4tut.pdf.
  54. R. N. Bhatt and P. A. Lee, “Scaling studies of highly disordered spin-1/2 antiferromagnetic systems,” Phys. Rev. Lett. 48 no. 5, (1982) 344–347.
  55. D. S. Fisher, “Random antiferromagnetic quantum spin chains,” Phys. Rev. B 50 no. 6, (1994) 3799–3821.
  56. F. Igloi and C. Monthus, “Strong disorder rg approach of random systems,” Physics Reports 412 no. 5–6, (2005) 277–431.
  57. G. Refael and J. E. Moore, “Entanglement Entropy of Random Quantum Critical Points in One Dimension,” Phys. Rev. Lett. 93 no. 26, (2004) 260602, arXiv:cond-mat/0406737.
  58. G. Refael and J. E. Moore, “Criticality and entanglement in random quantum systems,” Journal of Physics A: Mathematical and Theoretical 42 no. 50, (2009) 504010, arXiv:0908.1986 [cond-mat.dis-nn].
  59. A. Y. Kitaev, “Fault tolerant quantum computation by anyons,” Annals Phys. 303 (2003) 2–30, arXiv:quant-ph/9707021.
  60. K. Binder and A. P. Young, “Spin glasses: Experimental facts, theoretical concepts, and open questions,” Rev. Mod. Phys. 58 no. 4, (1986) 801–976.
  61. T. Castellani and A. Cavagna, “Spin-glass theory for pedestrians,” J. Phys. A 2005 no. 05, (2005) P05012.
  62. L. F. Cugliandolo and M. Mueller, “Quantum Glasses – a review,” arXiv:2208.05417 [cond-mat.dis-nn].
  63. P.-S. Hsin, L. V. Iliesiu, and Z. Yang, “A violation of global symmetries from replica wormholes and the fate of black hole remnants,” Class. Quant. Grav. 38 no. 19, (2021) 194004, arXiv:2011.09444 [hep-th].
  64. Y. Chen and H. W. Lin, “Signatures of global symmetry violation in relative entropies and replica wormholes,” JHEP 03 (2021) 040, arXiv:2011.06005 [hep-th].
  65. A. Belin and J. de Boer, “Random statistics of OPE coefficients and Euclidean wormholes,” Class. Quant. Grav. 38 no. 16, (2021) 164001, arXiv:2006.05499 [hep-th].
  66. P. Saad, S. H. Shenker, D. Stanford, and S. Yao, “Wormholes without averaging,” arXiv:2103.16754 [hep-th].
  67. Z. Komargodski, “The Constraints of Conformal Symmetry on RG Flows,” JHEP 07 (2012) 069, arXiv:1112.4538 [hep-th].
  68. R. Islam, R. Ma, P. M. Preiss, M. E. Tai, A. Lukin, M. Rispoli, and M. Greiner, “Measuring entanglement entropy through the interference of quantum many-body twins,” arXiv:1509.01160 [cond-mat.quant-gas].
  69. M. B. Hastings, “An area law for one-dimensional quantum systems,” J. Stat. Mech. 0708 (2007) P08024, arXiv:0705.2024 [quant-ph].
  70. J. Eisert, M. Cramer, and M. B. Plenio, “Area laws for the entanglement entropy - a review,” Rev. Mod. Phys. 82 (2010) 277–306, arXiv:0808.3773 [quant-ph].
  71. M. P. A. Fisher, V. Khemani, A. Nahum, and S. Vijay, “Random Quantum Circuits,” Ann. Rev. Condensed Matter Phys. 14 (2023) 335–379, arXiv:2207.14280 [quant-ph].
  72. P. Calabrese and J. Cardy, “Entanglement entropy and conformal field theory,” J. Phys. A 42 (2009) 504005, arXiv:0905.4013 [cond-mat.stat-mech].
  73. R. Vanhove, L. Lootens, M. Van Damme, R. Wolf, T. J. Osborne, J. Haegeman, and F. Verstraete, “Critical Lattice Model for a Haagerup Conformal Field Theory,” Phys. Rev. Lett. 128 no. 23, (2022) 231602, arXiv:2110.03532 [cond-mat.stat-mech].
  74. T.-C. Huang, Y.-H. Lin, K. Ohmori, Y. Tachikawa, and M. Tezuka, “Numerical Evidence for a Haagerup Conformal Field Theory,” Phys. Rev. Lett. 128 no. 23, (2022) 231603, arXiv:2110.03008 [cond-mat.stat-mech].
  75. I. Bengtsson and K. Życzkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement. Cambridge University Press, 2017.
  76. M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy. Lecture Notes in Physics. Springer International Publishing, 2017.
  77. J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2 (1998) 231–252, arXiv:hep-th/9711200.
  78. E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2 (1998) 253–291, arXiv:hep-th/9802150.
  79. O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, “Large N field theories, string theory and gravity,” Phys. Rept. 323 (2000) 183–386, arXiv:hep-th/9905111.
  80. S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96 (2006) 181602, arXiv:hep-th/0603001.
  81. D. Harlow and H. Ooguri, “Symmetries in quantum field theory and quantum gravity,” Commun. Math. Phys. 383 no. 3, (2021) 1669–1804, arXiv:1810.05338 [hep-th].
  82. M. Müller-Lennert, F. Dupuis, O. Szehr, S. Fehr, and M. Tomamichel, “On quantum Renyi entropies: a new generalization and some properties,” J. Math. Phys. 54 (2013) 122203, arXiv:1306.3142 [quant-ph].
  83. I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, “Interacting Electrons in Disordered Wires: Anderson Localization and Low-T Transport,” Phys. Rev. Lett. 95 no. 20, (2005) 206603.
  84. D. M. Basko, I. L. Aleiner, and B. L. Altshuler, “Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states,” Annals Phys. 321 no. 5, (2006) 1126–1205.
  85. R. Nandkishore and D. A. Huse, “Many body localization and thermalization in quantum statistical mechanics,” Ann. Rev. Condensed Matter Phys. 6 (2015) 15–38, arXiv:1404.0686 [cond-mat.stat-mech].
  86. D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, “Colloquium: Many-body localization, thermalization, and entanglement,” Rev. Mod. Phys. 91 (May, 2019) 021001.
  87. D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP 02 (2015) 172, arXiv:1412.5148 [hep-th].
  88. S. A. Parameswaran and R. Vasseur, “Many-body localization, symmetry, and topology,” Rept. Prog. Phys. 81 no. 8, (2018) 082501, arXiv:1801.07731 [cond-mat.dis-nn].
  89. S. Gopalakrishnan and S. A. Parameswaran, “Dynamics and Transport at the Threshold of Many-Body Localization,” Phys. Rept. 862 (2020) 1–62, arXiv:1908.10435 [cond-mat.dis-nn].
  90. M. Freedman and M. Headrick, “Bit threads and holographic entanglement,” Commun. Math. Phys. 352 no. 1, (2017) 407–438, arXiv:1604.00354 [hep-th].
  91. M.-D. Choi, “Completely positive linear maps on complex matrices,” Linear Algebra Appl. 10 no. 3, (1975) 285–290.
  92. H. Bernien et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551 (2017) 579–584, arXiv:1707.04344 [quant-ph].
  93. S. Moudgalya, S. Rachel, B. A. Bernevig, and N. Regnault, “Exact excited states of nonintegrable models,” Phys. Rev. B 98 no. 23, (2018) 235155.
  94. M. Serbyn, D. A. Abanin, and Z. Papić, “Quantum many-body scars and weak breaking of ergodicity,” Nature Phys. 17 no. 6, (2021) 675–685, arXiv:2011.09486 [quant-ph].
  95. S. Moudgalya, B. A. Bernevig, and N. Regnault, “Quantum many-body scars and Hilbert space fragmentation: a review of exact results,” Rept. Prog. Phys. 85 no. 8, (2022) 086501, arXiv:2109.00548 [cond-mat.str-el].
  96. K. Pakrouski, P. N. Pallegar, F. K. Popov, and I. R. Klebanov, “Many Body Scars as a Group Invariant Sector of Hilbert Space,” Phys. Rev. Lett. 125 no. 23, (2020) 230602, arXiv:2007.00845 [cond-mat.str-el].
  97. M. Medenjak, B. Buča, and D. Jaksch, “Isolated Heisenberg magnet as a quantum time crystal,” Phys. Rev. B 102 no. 4, (2020) 041117.
  98. N. O’Dea, F. Burnell, A. Chandran, and V. Khemani, “From tunnels to towers: quantum scars from Lie Algebras and q-deformed Lie Algebras,” Phys. Rev. Res. 2 no. 4, (2020) 043305, arXiv:2007.16207 [cond-mat.stat-mech].
  99. J. Ren, C. Liang, and C. Fang, “Quasisymmetry Groups and Many-Body Scar Dynamics,” Phys. Rev. Lett. 126 no. 12, (2021) 120604, arXiv:2007.10380 [cond-mat.str-el].
  100. P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Pollmann, “Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians,” Phys. Rev. X 10 no. 1, (2020) 011047, arXiv:1904.04266 [cond-mat.str-el].
  101. V. Khemani, M. Hermele, and R. Nandkishore, “Localization from Hilbert space shattering: From theory to physical realizations,” Phys. Rev. B 101 no. 17, (2020) 174204, arXiv:1904.04815 [cond-mat.stat-mech].
  102. S. Moudgalya, A. Prem, R. Nandkishore, N. Regnault, and B. A. Bernevig, “Thermalization and Its Absence within Krylov Subspaces of a Constrained Hamiltonian,” in Memorial Volume for Shoucheng Zhang, pp. 147–209. World Scientific, 2021. arXiv:1910.14048 [cond-mat.str-el].
  103. L. Zadnik and M. Fagotti, “The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties,” SciPost Phys. Core 4 (2021) 010, arXiv:2009.04995 [cond-mat.stat-mech].
  104. K. Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, “Volume of the set of separable states,” Phys. Rev. A 58 (1998) 883, arXiv:quant-ph/9804024.
  105. P. Calabrese, J. Cardy, and E. Tonni, “Entanglement negativity in quantum field theory,” Phys. Rev. Lett. 109 (2012) 130502, arXiv:1206.3092 [cond-mat.stat-mech].
  106. Y. A. Lee and G. Vidal, “Entanglement negativity and topological order,” Phys. Rev. A 88 no. 4, (2013) 042318.
  107. S. Sang, Y. Li, T. Zhou, X. Chen, T. H. Hsieh, and M. P. A. Fisher, “Entanglement Negativity at Measurement-Induced Criticality,” PRX Quantum 2 no. 3, (2021) 030313, arXiv:2012.00031 [cond-mat.stat-mech].
  108. E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory,” J. Math. Phys. 43 (2002) 4452–4505, arXiv:quant-ph/0110143.
  109. Y. Bao, R. Fan, A. Vishwanath, and E. Altman, “Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions,” arXiv:2301.05687 [quant-ph].
  110. R. Fan, Y. Bao, E. Altman, and A. Vishwanath, “Diagnostics of mixed-state topological order and breakdown of quantum memory,” arXiv:2301.05689 [quant-ph].
  111. J. Y. Lee, C.-M. Jian, and C. Xu, “Quantum Criticality Under Decoherence or Weak Measurement,” PRX Quantum 4 no. 3, (2023) 030317, arXiv:2301.05238 [cond-mat.stat-mech].
  112. I. H. Kim, M. Levin, T.-C. Lin, D. Ranard, and B. Shi, “Universal Lower Bound on Topological Entanglement Entropy,” Phys. Rev. Lett. 131 no. 16, (2023) 166601, arXiv:2302.00689 [quant-ph].
  113. H. Casini and M. Huerta, “A Finite entanglement entropy and the c-theorem,” Phys. Lett. B 600 (2004) 142–150, arXiv:hep-th/0405111.
  114. H. Casini and M. Huerta, “A c-theorem for the entanglement entropy,” J. Phys. A 40 (2007) 7031–7036, arXiv:cond-mat/0610375.
  115. H. Casini and M. Huerta, “On the RG running of the entanglement entropy of a circle,” Phys. Rev. D 85 (2012) 125016, arXiv:1202.5650 [hep-th].
  116. S. N. Solodukhin, “The a-theorem and entanglement entropy,” arXiv:1304.4411 [hep-th].
  117. T. Nishioka, “Entanglement entropy: holography and renormalization group,” Rev. Mod. Phys. 90 no. 3, (2018) 035007, arXiv:1801.10352 [hep-th].
  118. D. Aasen, P. Fendley, and R. S. K. Mong, “Topological Defects on the Lattice: Dualities and Degeneracies,” arXiv:2008.08598 [cond-mat.stat-mech].
  119. A. Feiguin, S. Trebst, A. W. W. Ludwig, M. Troyer, A. Kitaev, Z. Wang, and M. H. Freedman, “Interacting anyons in topological quantum liquids: The golden chain,” Phys. Rev. Lett. 98 (2007) 160409, arXiv:cond-mat/0612341.
  120. S. Trebst, M. Troyer, Z. Wang, and A. W. W. Ludwig, “A short introduction to fibonacci anyon models,” Progress of Theoretical Physics Supplement 176 (2008) 384–407, arXiv:0902.3275 [cond-mat.stat-mech].
  121. M. Koide, Y. Nagoya, and S. Yamaguchi, “Non-invertible topological defects in 4-dimensional ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT pure lattice gauge theory,” PTEP 2022 no. 1, (2022) 013B03, arXiv:2109.05992 [hep-th].
  122. Y. Choi, C. Cordova, P.-S. Hsin, H. T. Lam, and S.-H. Shao, “Noninvertible duality defects in 3+1 dimensions,” Phys. Rev. D 105 no. 12, (2022) 125016, arXiv:2111.01139 [hep-th].
  123. C. Cordova, P.-S. Hsin, and C. Zhang, “Anomalies of Non-Invertible Symmetries in (3+1)d,” arXiv:2308.11706 [hep-th].
  124. L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry,” Phys. Rev. Res. 2 no. 4, (2020) 043086, arXiv:2005.14178 [cond-mat.str-el].
  125. J. Kaidi, K. Ohmori, and Y. Zheng, “Symmetry TFTs for Non-invertible Defects,” Commun. Math. Phys. 404 no. 2, (2023) 1021–1124, arXiv:2209.11062 [hep-th].
  126. D. S. Freed, G. W. Moore, and C. Teleman, “Topological symmetry in quantum field theory,” arXiv:2209.07471 [hep-th].
  127. C. Zhang and C. Córdova, “Anomalies of (1+1)⁢D11𝐷(1+1)D( 1 + 1 ) italic_D categorical symmetries,” arXiv:2304.01262 [cond-mat.str-el].
  128. Y.-N. Zhou, X. Li, H. Zhai, C. Li, and Y. Gu, “Reviving the Lieb–Schultz–Mattis Theorem in Open Quantum Systems,” arXiv:2310.01475 [cond-mat.str-el].
Citations (14)
View on Semantic Scholar

Summary

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

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

Tweets