- Letter
- Open Access
Exceptional dynamics of interacting spin liquids
Phys. Rev. Research 4, L042025 – Published 14 November, 2022
DOI: https://doi.org/10.1103/PhysRevResearch.4.L042025
Abstract
We show that interactions in quantum spin liquids can result in non-Hermitian phenomenology that differs qualitatively from mean-field expectations. We demonstrate this in two prominent cases through the effects of phonons and disorder on a Kitaev honeycomb model. Using analytic and numerical calculations, we show the generic appearance of exceptional points and rings depending on the symmetry of the system. Their existence is reflected in dynamical observables including the dynamic structure function measured in neutron scattering. The results point to different phenomenological features in realizable spin liquids that must be incorporated into the analysis of experimental data and also indicate that spin liquids could be generically stable to wider classes of perturbations.
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References (67)
- P. W. Anderson, The resonating valence bond state in and superconductivity, Science 235, 1196 (1987).
- L. Balents, Spin liquids in frustrated magnets, Nature (London) 464, 199 (2010).
- L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
- J. Knolle and R. Moessner, A field guide to spin liquids, Annu. Rev. Condens. Matter Phys. 10, 451 (2019).
- K. Yang, S.-H. Phark, Y. Bae, T. Esat, P. Willke, A. Ardavan, A. J. Heinrich, and C. P. Lutz, Probing resonating valence bond states in artificial quantum magnets, Nat. Commun. 12, 1 (2021).
- R. Sibille, E. Lhotel, M. Ciomaga Hatnean, G. J. Nilsen, G. Ehlers, A. Cervellino, E. Ressouche, M. Frontzek, O. Zaharko, V. Pomjakushin et al., Coulomb spin liquid in anion-disordered pyrochlore , Nat. Commun. 8, 892 (2017).
- I. Kimchi, A. Nahum, and T. Senthil, Valence Bonds in Random Quantum Magnets: Theory and Application to , Phys. Rev. X 8, 031028 (2018).
- T.-H. Han, M. R. Norman, J.-J. Wen, J. A. Rodriguez-Rivera, J. S. Helton, C. Broholm, and Y. S. Lee, Correlated impurities and intrinsic spin-liquid physics in the kagome material herbertsmithite, Phys. Rev. B 94, 060409 (2016)(R).
- H. B. Cao, A. Banerjee, J.-Q. Yan, C. A. Bridges, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, B. C. Chakoumakos, and S. E. Nagler, Low-temperature crystal and magnetic structure of , Phys. Rev. B 93, 134423 (2016).
- Z. Zhu, P. A. Maksimov, S. R. White, and A. L. Chernyshev, Disorder-Induced Mimicry of a Spin Liquid in , Phys. Rev. Lett. 119, 157201 (2017).
- Y. Li, D. Adroja, R. I. Bewley, D. Voneshen, A. A. Tsirlin, P. Gegenwart, and Q. Zhang, Crystalline Electric-Field Randomness in the Triangular Lattice Spin-Liquid , Phys. Rev. Lett. 118, 107202 (2017).
- C. M. Pasco, B. A. Trump, T. T. Tran, Z. A. Kelly, C. Hoffmann, I. Heinmaa, R. Stern, and T. M. McQueen, Single-crystal growth of and universal behavior in quantum spin liquid candidates synthetic barlowite and herbertsmithite, Phys. Rev. Mater. 2, 044406 (2018).
- S.-S. Lee, Low-energy effective theory of Fermi surface coupled with U(1) gauge field in dimensions, Phys. Rev. B 80, 165102 (2009).
- D. F. Mross, J. McGreevy, H. Liu, and T. Senthil, Controlled expansion for certain non-fermi-liquid metals, Phys. Rev. B 82, 045121 (2010).
- S.-S. Lee and P. A. Lee, U(1) Gauge Theory of the Hubbard Model: Spin Liquid States and Possible Application to , Phys. Rev. Lett. 95, 036403 (2005).
- S. C. Morampudi, A. M. Turner, F. Pollmann, and F. Wilczek, Statistics of Fractionalized Excitations through Threshold Spectroscopy, Phys. Rev. Lett. 118, 227201 (2017).
- S. C. Morampudi, F. Wilczek, and C. R. Laumann, Spectroscopy of Spinons in Coulomb Quantum Spin Liquids, Phys. Rev. Lett. 124, 097204 (2020).
- S. D. Pace, S. C. Morampudi, R. Moessner, and C. R. Laumann, Emergent Fine Structure Constant of Quantum Spin Ice Is Large, Phys. Rev. Lett. 127, 117205 (2021).
- E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
- Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Topological Phases of Non-Hermitian Systems, Phys. Rev. X 8, 031079 (2018).
- H. Shen and L. Fu, Quantum Oscillation from In-Gap States and a Non-Hermitian Landau Level Problem, Phys. Rev. Lett. 121, 026403 (2018).
- Y. Nagai, Y. Qi, H. Isobe, V. Kozii, and L. Fu, DMFT Reveals the Non-Hermitian Topology and Fermi Arcs in Heavy-Fermion Systems, Phys. Rev. Lett. 125, 227204 (2020).
- M. Papaj, H. Isobe, and L. Fu, Nodal arc of disordered Dirac fermions and non-Hermitian band theory, Phys. Rev. B 99, 201107(R) (2019).
- T. Matsushita, Y. Nagai, and S. Fujimoto, Disorder-induced exceptional and hybrid point rings in Weyl/Dirac semimetals, Phys. Rev. B 100, 245205 (2019).
- A. A. Zyuzin and P. Simon, Disorder-induced exceptional points and nodal lines in Dirac superconductors, Phys. Rev. B 99, 165145 (2019).
- T. Yoshida, R. Peters, N. Kawakami, and Y. Hatsugai, Exceptional band touching for strongly correlated systems in equilibrium, Prog. Theor. Exp. Phys. 2020, 12A109 (2020).
- B. Michen, T. Micallo, and J. C. Budich, Exceptional non-Hermitian phases in disordered quantum wires, Phys. Rev. B 104, 035413 (2021).
- L. Crippa, J. C. Budich, and G. Sangiovanni, Fourth-order exceptional points in correlated quantum many-body systems, Phys. Rev. B 104, L121109 (2021).
- Y. Michishita, T. Yoshida, and R. Peters, Relationship between exceptional points and the Kondo effect in -electron materials, Phys. Rev. B 101, 085122 (2020).
- G. Jackeli and G. Khaliullin, Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models, Phys. Rev. Lett. 102, 017205 (2009).
- H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, and S. E. Nagler, Concept and realization of Kitaev quantum spin liquids, Nat. Rev. Phys. 1, 264 (2019).
- A. Banerjee, J. Yan, J. Knolle, C. A. Bridges, M. B. Stone, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, R. Moessner, and S. E. Nagler, Neutron scattering in the proximate quantum spin liquid -RuCl3, Science 356, 1055 (2017).
- K. Kitagawa, T. Takayama, Y. Matsumoto, A. Kato, R. Takano, Y. Kishimoto, S. Bette, R. Dinnebier, G. Jackeli, and H. Takagi, A spin–orbital-entangled quantum liquid on a honeycomb lattice, Nature (London) 554, 341 (2018).
- Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Motome et al., Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid, Nature (London) 559, 227 (2018).
- Y. Vinkler-Aviv and A. Rosch, Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons, Phys. Rev. X 8, 031032 (2018).
- M. Ye, G. B. Halász, L. Savary, and L. Balents, Quantization of the Thermal Hall Conductivity at Small Hall Angles, Phys. Rev. Lett. 121, 147201 (2018).
- J. G. Rau, E. K.-H. Lee, and H.-Y. Kee, Spin-orbit physics giving rise to novel phases in correlated systems: Iridates and related materials, Annu. Rev. Condens. Matter Phys. 7, 195 (2016).
- M. Gohlke, G. Wachtel, Y. Yamaji, F. Pollmann, and Y. B. Kim, Quantum spin liquid signatures in Kitaev-like frustrated magnets, Phys. Rev. B 97, 075126 (2018).
- M. Hermanns, I. Kimchi, and J. Knolle, Physics of the Kitaev model: Fractionalization, dynamic correlations, and material connections, Annu. Rev. Condens. Matter Phys. 9, 17 (2018).
- M. Berry, Physics of nonhermitian degeneracies, Czech. J. Phys. 54, 1039 (2004).
- K. Yang, S. C. Morampudi, and E. J. Bergholtz, Exceptional Spin Liquids from Couplings to the Environment, Phys. Rev. Lett. 126, 077201 (2021).
- M. Peskin, An Introduction To Quantum Field Theory (CRC Press, Boca Raton, FL, 2018).
- X. Wen, Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons, Oxford Graduate Texts (Oxford University Press, Oxford, U.K., 2007).
- K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Symmetry and Topology in Non-Hermitian Physics, Phys. Rev. X 9, 041015 (2019).
- J. C. Budich, J. Carlström, F. K. Kunst, and E. J. Bergholtz, Symmetry-protected nodal phases in non-Hermitian systems, Phys. Rev. B 99, 041406(R) (2019).
- T. Yoshida, R. Peters, N. Kawakami, and Y. Hatsugai, Symmetry-protected exceptional rings in two-dimensional correlated systems with chiral symmetry, Phys. Rev. B 99, 121101(R) (2019).
- A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321, 2 (2006).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L042025 for details of symmetry transformation, degeneracy for Dirac fermions, calculations of correlation functions, random magnetic field realizations and numerical disordered results.
- A. J. Willans, J. T. Chalker, and R. Moessner, Disorder in a Quantum Spin Liquid: Flux Binding and Local Moment Formation, Phys. Rev. Lett. 104, 237203 (2010).
- A. J. Willans, J. T. Chalker, and R. Moessner, Site dilution in the Kitaev honeycomb model, Phys. Rev. B 84, 115146 (2011).
- D. Otten, A. Roy, and F. Hassler, Dynamical structure factor in the non-Abelian phase of the Kitaev honeycomb model in the presence of quenched disorder, Phys. Rev. B 99, 035137 (2019).
- F. Zschocke and M. Vojta, Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape, Phys. Rev. B 92, 014403 (2015).
- J. Knolle, R. Moessner, and N. B. Perkins, Bond-Disordered Spin Liquid and the Honeycomb Iridate : Abundant Low-Energy Density of States from Random Majorana Hopping, Phys. Rev. Lett. 122, 047202 (2019).
- A. Weiße, G. Wellein, A. Alvermann, and H. Fehske, The kernel polynomial method, Rev. Mod. Phys. 78, 275 (2006).
- D. Varjas, M. Fruchart, A. R. Akhmerov, and P. M. Perez-Piskunow, Computation of topological phase diagram of disordered using the kernel polynomial method, Phys. Rev. Res. 2, 013229 (2020).
- K. Feng, N. B. Perkins, and F. J. Burnell, Further insights into the thermodynamics of the Kitaev honeycomb model, Phys. Rev. B 102, 224402 (2020).
- W.-H. Kao, J. Knolle, G. B. Halász, R. Moessner, and N. B. Perkins, Vacancy-Induced Low-Energy Density of States in the Kitaev Spin Liquid, Phys. Rev. X 11, 011034 (2021).
- A. Metavitsiadis, W. Natori, J. Knolle, and W. Brenig, Optical phonons coupled to a Kitaev spin liquid, Phys. Rev. B 105, 165151 (2022).
- A. Metavitsiadis and W. Brenig, Phonon renormalization in the Kitaev quantum spin liquid, Phys. Rev. B 101, 035103 (2020).
- M. Ye, R. M. Fernandes, and N. B. Perkins, Phonon dynamics in the kitaev spin liquid, Phys. Rev. Res. 2, 033180 (2020).
- X.-Y. Song, Y.-Z. You, and L. Balents, Low-Energy Spin Dynamics of the Honeycomb Spin Liquid Beyond the Kitaev Limit, Phys. Rev. Lett. 117, 037209 (2016).
- Y. Wan and N. P. Armitage, Resolving Continua of Fractional Excitations by Spinon Echo in THz 2D Coherent Spectroscopy, Phys. Rev. Lett. 122, 257401 (2019).
- W. Choi, K. H. Lee, and Y. B. Kim, Theory of Two-Dimensional Nonlinear Spectroscopy for the Kitaev Spin Liquid, Phys. Rev. Lett. 124, 117205 (2020).
- R. M. Nandkishore, W. Choi, and Y. B. Kim, Spectroscopic fingerprints of gapped quantum spin liquids, both conventional and fractonic, Phys. Rev. Res. 3, 013254 (2021).
- M. Kanega, T. N. Ikeda, and M. Sato, Linear and nonlinear optical responses in Kitaev spin liquids, Phys. Rev. Res. 3, L032024 (2021).
- Z.-L. Li, M. Oshikawa, and Y. Wan, Photon Echo from Lensing of Fractional Excitations in Tomonaga-Luttinger Spin Liquid, Phys. Rev. X 11, 031035 (2021).
- J. Carlström, M. Stålhammar, J. C. Budich, and E. J. Bergholtz, Knotted non-Hermitian metals, Phys. Rev. B 99, 161115(R) (2019).