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Monopoles in Dirac spin liquids and their symmetries from instanton calculus (2310.06748v2)

Published 10 Oct 2023 in cond-mat.str-el and hep-th

Abstract: The Dirac spin liquid (DSL) is a two-dimensional (2D) fractionalized Mott insulator featuring massless Dirac spinon excitations coupled to a compact $U(1)$ gauge field, which allows for flux-tunneling instanton events described by magnetic monopoles in (2+1)D Euclidean spacetime. The state-operator correspondence of conformal field theory has been used recently to define associated monopole operators and determine their quantum numbers, which encode the microscopic symmetries of conventional ordered phases proximate to the DSL. In this work, we utilize semiclassical instanton methods not relying on conformal invariance to construct monopole operators directly in (2+1)D spacetime as instanton-induced 't Hooft vertices, i.e., fermion-number-violating effective interactions originating from zero modes of the Euclidean Dirac operator in an instanton background. In the presence of a flavor-adjoint fermion mass, resummation of the instanton gas is shown to select the correct monopole to be proliferated, in accordance with predictions of the state-operator correspondence. We also show that our instanton-based approach is able to determine monopole quantum numbers on bipartite lattices.

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References (59)
  1. L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80(1), 016502 (2016), 10.1088/0034-4885/80/1/016502.
  2. X.-G. Wen, Quantum orders and symmetric spin liquids, Phys. Rev. B 65, 165113 (2002), 10.1103/PhysRevB.65.165113.
  3. X. G. Wen, Mean-field theory of spin-liquid states with finite energy gap and topological orders, Phys. Rev. B 44(6), 2664 (1991), 10.1103/PhysRevB.44.2664.
  4. X.-G. Wen, Quantum Field Theory of Many-Body Systems, Oxford University Press, Oxford (2007).
  5. Algebraic spin liquid as the mother of many competing orders, Phys. Rev. B 72(10), 104404 (2005), 10.1103/PhysRevB.72.104404.
  6. M. B. Hastings, Dirac structure, RVB, and Goldstone modes in the kagomé antiferromagnet, Phys. Rev. B 63(1), 014413 (2000), 10.1103/PhysRevB.63.014413.
  7. Projected-Wave-Function Study of the Spin-1/2121/21 / 2 Heisenberg Model on the Kagomé Lattice, Phys. Rev. Lett. 98(11), 117205 (2007), 10.1103/PhysRevLett.98.117205.
  8. Properties of an algebraic spin liquid on the kagome lattice, Phys. Rev. B 77(22), 224413 (2008), 10.1103/PhysRevB.77.224413.
  9. Unifying description of competing orders in two-dimensional quantum magnets, Nat. Commun. 10(1), 4254 (2019), 10.1038/s41467-019-11727-3.
  10. From spinon band topology to the symmetry quantum numbers of monopoles in dirac spin liquids, Phys. Rev. X 10(1), 011033 (2020), 10.1103/PhysRevX.10.011033.
  11. Monte carlo study of lattice compact quantum electrodynamics with fermionic matter: The parent state of quantum phases, Phys. Rev. X 9, 021022 (2019), 10.1103/PhysRevX.9.021022.
  12. Stability of U(1) spin liquids in two dimensions, Phys. Rev. B 70(21), 214437 (2004), 10.1103/PhysRevB.70.214437.
  13. A. M. Polyakov, Compact gauge fields and the infrared catastrophe, Phys. Lett. B 59(1), 82 (1975), https://doi.org/10.1016/0370-2693(75)90162-8.
  14. A. M. Polyakov, Quark confinement and topology of gauge theories, Nucl. Phys. B 120(3), 429 (1977), 10.1016/0550-3213(77)90086-4.
  15. A. M. Polyakov, Gauge Fields and Strings, Routledge, New York (2021).
  16. V. Borokhov, A. Kapustin and X. Wu, Topological Disorder Operators in Three-Dimensional Conformal Field Theory, JHEP 11(11), 049 (2002), 10.1088/1126-6708/2002/11/049.
  17. T. Grover, Entanglement Monotonicity and the Stability of Gauge Theories in Three Spacetime Dimensions, Phys. Rev. Lett. 112(15), 151601 (2014), 10.1103/PhysRevLett.112.151601.
  18. S. S. Pufu, Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics, Phys. Rev. D 89(6), 065016 (2014), 10.1103/PhysRevD.89.065016.
  19. Criticality in quantum triangular antiferromagnets via fermionized vortices, Phys. Rev. B 72(6), 064407 (2005), 10.1103/PhysRevB.72.064407.
  20. J. Alicea, O. I. Motrunich and M. P. A. Fisher, Algebraic Vortex Liquid in Spin-1/2121/21 / 2 Triangular Antiferromagnets: Scenario for Cs2⁢CuCl4subscriptnormal-Cs2subscriptnormal-CuCl4\mathrm{Cs}_{2}\mathrm{CuCl}_{4}roman_Cs start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT roman_CuCl start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT, Phys. Rev. Lett. 95(24), 247203 (2005), 10.1103/PhysRevLett.95.247203.
  21. J. Alicea, O. I. Motrunich and M. P. A. Fisher, Theory of the algebraic vortex liquid in an anisotropic spin-1/2121/21 / 2 triangular antiferromagnet, Phys. Rev. B 73(17), 174430 (2006), 10.1103/PhysRevB.73.174430.
  22. J. Alicea, Monopole quantum numbers in the staggered flux spin liquid, Phys. Rev. B 78(3), 035126 (2008), 10.1103/PhysRevB.78.035126.
  23. R. Jackiw, Fractional charge and zero modes for planar systems in a magnetic field, Phys. Rev. D 29(10), 2375 (1984), 10.1103/PhysRevD.29.2375.
  24. G. Shankar and J. Maciejko, Symmetry-breaking effects of instantons in parton gauge theories, Phys. Rev. B 104(3), 035134 (2021), 10.1103/PhysRevB.104.035134.
  25. Spin-peierls instability of the U(1) dirac spin liquid, arXiv:2307.12295 (2023), https://arxiv.org/abs/2307.12295.
  26. G. Nambiar, D. Bulmash and V. Galitski, Monopole Josephson effects in a Dirac spin liquid, Phys. Rev. Research 5(1), 013169 (2023), 10.1103/PhysRevResearch.5.013169.
  27. Monopoles in CPN−1superscriptnormal-CP𝑁1\mathrm{CP}^{N-1}roman_CP start_POSTSUPERSCRIPT italic_N - 1 end_POSTSUPERSCRIPT model via the state-operator correspondence, Phys. Rev. B 78(21), 214418 (2008), 10.1103/PhysRevB.78.214418.
  28. S. S. Pufu and S. Sachdev, Monopoles in 2 + 1-dimensional conformal field theories with global U(1) symmetry, JHEP 09, 127 (2013), 10.1007/JHEP09(2013)127.
  29. Monopole Taxonomy in three-dimensional conformal field theories, arXiv:1309.1160 (2013), https://arxiv.org/abs/1309.1160.
  30. Scaling dimensions of monopole operators in the CPN−1superscriptnormal-CP𝑁1\mathrm{CP}^{N-1}roman_CP start_POSTSUPERSCRIPT italic_N - 1 end_POSTSUPERSCRIPT theory in 2+1212+12 + 1 dimensions, JHEP 06, 037 (2015), 10.1007/JHEP06(2015)037.
  31. Monopole operators from the 4−ϵ4italic-ϵ4-\epsilon4 - italic_ϵ expansion, JHEP 12(12), 015 (2016), 10.1007/JHEP12(2016)015.
  32. Monopole operators in U(1) Chern-Simons-matter theories, JHEP 05, 157 (2018), 10.1007/JHEP05(2018)157.
  33. Transition between algebraic and ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT quantum spin liquids at large N, Phys. Rev. B 98(3), 035137 (2018), 10.1103/PhysRevB.98.035137.
  34. Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a 𝑄𝐸𝐷3subscript𝑄𝐸𝐷3\textrm{QED}_{3}QED start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT-Gross-Neveu theory, Phys. Rev. B 100(9), 094443 (2019), 10.1103/PhysRevB.100.094443.
  35. É. Dupuis and W. Witczak-Krempa, Monopole hierarchy in transitions out of a Dirac spin liquid, Ann. Phys. 435, 168496 (2021), 10.1016/j.aop.2021.168496.
  36. É. Dupuis, R. Boyack and W. Witczak-Krempa, Anomalous Dimensions of Monopole Operators at the Transitions between Dirac and Topological Spin Liquids, Phys. Rev. X 12(3), 031012 (2022), 10.1103/PhysRevX.12.031012.
  37. Evidence for 3d bosonization from monopole operators, arXiv:2210.12370 (2022), http://arxiv.org/abs/2210.12370.
  38. C. Xu, Renormalization group studies on four-fermion interaction instabilities on algebraic spin liquids, Phys. Rev. B 78(5), 054432 (2008), 10.1103/PhysRevB.78.054432.
  39. G. Murthy and S. Sachdev, Action of hedgehog instantons in the disordered phase of the (2+1)21(2+1)( 2 + 1 )-dimensional CPN−1superscriptnormal-CP𝑁1\mathrm{CP}^{N-1}roman_CP start_POSTSUPERSCRIPT italic_N - 1 end_POSTSUPERSCRIPT model, Nucl. Phys. B 344(3), 557 (1990), 10.1016/0550-3213(90)90670-9.
  40. M. Ünsal, Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions, Phys. Rev. D 80(6), 065001 (2009), 10.1103/PhysRevD.80.065001.
  41. Continuous transition between Ising magnetic order and a chiral spin liquid, Phys. Rev. B 106(24), 245107 (2022), 10.1103/PhysRevB.106.245107.
  42. I. Affleck, J. Harvey and E. Witten, Instantons and (super-) symmetry breaking in (2+1) dimensions, Nucl. Phys. B 206(3), 413 (1982), 10.1016/0550-3213(82)90277-2.
  43. G. ’t Hooft, Symmetry Breaking through Bell-Jackiw Anomalies, Phys. Rev. Lett. 37(1), 8 (1976), 10.1103/PhysRevLett.37.8.
  44. G. ’t Hooft, Computation of the quantum effects due to a four-dimensional pseudoparticle, Phys. Rev. D 14(12), 3432 (1976), 10.1103/PhysRevD.14.3432.
  45. G. ’t Hooft, How instantons solve the U(1) problem, Phys. Rep. 142(6), 357 (1986), 10.1016/0370-1573(86)90117-1.
  46. Concept and realization of Kitaev quantum spin liquids, Nat. Rev. Phys. 1(4), 264 (2019), 10.1038/s42254-019-0038-2.
  47. C. Mudry and E. Fradkin, Separation of spin and charge quantum numbers in strongly correlated systems, Phys. Rev. B 49(8), 5200 (1994), 10.1103/PhysRevB.49.5200.
  48. Theory of Spin Excitations in Undoped and Underdoped Cuprates, Ann. Phys. 272(1), 130 (1999), 10.1006/aphy.1998.5888.
  49. W. Rantner and X.-G. Wen, Spin correlations in the algebraic spin liquid: Implications for high-Tcsubscriptnormal-T𝑐\mathrm{T}_{c}roman_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT superconductors, Phys. Rev. B 66(14), 144501 (2002), 10.1103/PhysRevB.66.144501.
  50. J. B. Marston, Instantons and massless fermions in (2+1)-dimensional lattice QED and antiferromagnets, Phys. Rev. Lett. 64(10), 1166 (1990), 10.1103/PhysRevLett.64.1166.
  51. R. Jackiw and C. Rebbi, Solitons with fermion number ½, Phys. Rev. D 13, 3398 (1976), 10.1103/PhysRevD.13.3398.
  52. K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s functions, Commun. Math. Phys. 31(2), 83 (1973), 10.1007/BF01645738.
  53. C. Wetterich, Spinors in euclidean field theory, complex structures and discrete symmetries, Nucl. Phys. B 852(1), 174 (2011), 10.1016/j.nuclphysb.2011.06.013.
  54. Dirac monopole without strings: Monopole harmonics, Nucl. Phys. B 107(3), 365 (1976), 10.1016/0550-3213(76)90143-7.
  55. E. Witten, Fermion path integrals and topological phases, Rev. Mod. Phys. 88(3), 035001 (2016), 10.1103/RevModPhys.88.035001.
  56. Time-reversal symmetry, anomalies, and dualities in (2+1)d𝑑ditalic_d, SciPost Phys. 5(1), 006 (2018), 10.21468/SciPostPhys.5.1.006.
  57. Y.-M. Lu, G. Y. Cho and A. Vishwanath, Unification of bosonic and fermionic theories of spin liquids on the kagomé lattice, Phys. Rev. B 96(20), 205150 (2017), 10.1103/PhysRevB.96.205150.
  58. M. Hermele, SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice, Phys. Rev. B 76(3), 035125 (2007), 10.1103/PhysRevB.76.035125.
  59. M. Stone, Supersymmetry and the quantum mechanics of spin, Nucl. Phys. B 314(3), 557 (1989), 10.1016/0550-3213(89)90408-2.

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