Comment on "Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice" (Punk, M., Chowdhury, D. & Sachdev, S. Nature Physics 10, 289-293 (2014))
V. R. Shaginyan, M. Ya. Amusia, J. W. Clark, G. S. Japaridze, A. Z. Msezane, K. G. Popov, V. A. Stephanovich, M. V. Zverev, V. A. Khodel
aa r X i v : . [ c ond - m a t . s t r- e l ] S e p Comment on ”Topological excitations and the dynamic structure factor of spin liquidson the kagome lattice” (Punk, M., Chowdhury, D. & Sachdev, S. Nature Physics 10,289-293 (2014))
V. R. Shaginyan,
1, 2, ∗ M. Ya. Amusia,
3, 4
J. W. Clark, G. S. Japaridze, A. Z.Msezane, K. G. Popov, V. A. Stephanovich, M. V. Zverev,
8, 9 and V. A. Khodel
8, 5 Petersburg Nuclear Physics Institute, Gatchina, 188300, Russia Clark Atlanta University, Atlanta, GA 30314, USA Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel Ioffe Physical Technical Institute, RAS, St. Petersburg 194021, Russia McDonnell Center for the Space Sciences & Department of Physics,Washington University, St. Louis, MO 63130, USA Komi Science Center, Ural Division, RAS, Syktyvkar, 167982, Russia Opole University, Institute of Physics, Opole, 45-052, Poland Russian Research Center Kurchatov Institute, Moscow, 123182, Russia Moscow Institute of Physics and Technology, Moscow, 123098, Russia
Letter to the Editor — The authors of a recent pa-per [1] evidently take the view that the whole of progressmade toward a theoretical understanding of the physicsof quantum spin liquids (QSL) is associated with modelsof the kind proposed and applied in their present work.As motivation for this work, they observe that in contrastto existing theoretical models of both gapped and gaplessspin liquids, which give rise to sharp dispersive featuresin the dynamic structure factor, the measured dynamicstructure factor reveals an excitation continuum that isremarkably flat as a function of frequency. They go on toassert that “so far, the only theoretical model for a spinliquid state on the kagome lattice which naturally givesrise to a flat excitation band at low energies consists ofthe Z spin liquids”, cited as references 2 to 4.Here we point out that there already exists a differentand demonstrably successful approach to the QSL prob-lem that does naturally feature a flat band. This alterna-tive approach is based on the theory of fermion condensa-tion [2], which is concerned with special solutions admit-ted by the equations of the original Landau theory. Suchsolutions exhibit a fermion condensate (FC), composedof the totality of single-particle states belonging to a por-tion of the spectrum that is completely flat in some regionof momentum space [3]. It has been shown by Volovik[4] that solutions having a FC belong to a different topo-logical class of Fermi liquids than the conventional ones,even without the visons introduced by the authors of [1]as ”topology carriers”. Importantly, the effective massof a Landau quasiparticle now acquires a dependence onexternal parameters. This further development of theoriginal Landau theory provides for studies of charac-teristic non-Fermi-liquid behavior of FC-hosting systemsthat are associated with dramatic change of the single-particle spectrum under tiny variations of input param-eters, including temperature, magnetic field, pressure,doping, etc. In dealing with QSLs, such an approach al-lows one to gain insight into the physical mechanism op- erative in herbertsmithite, within the much broader con-text of similar phenomena in heavy-fermion (HF) metalsand quasicrystals. Notably, it permits one to calculatethe thermodynamic and relaxation properties of QSL asfunctions of temperature T and magnetic field B . Thecrux of the matter within the Landau-theoretic frame-work is that the kagome lattice of herbertsmithite sup-ports a strongly correlated QSL located at the fermion-condensation quantum phase transition point [2, 5, 6].The consequences of this conclusion are in good agree-ment with recent experimental data. Moreover, the un-usual behavior exhibited in QSL is seen to have univer-sal character, shared with that observed in such differentstrongly correlated fermionic systems as HF metals (in-cluding the quantum critical metal Sr Ru O , 2D He)and quasicrystals [2, 7, 8].The FC theory gives a consistent, even quantitative,account of many of the physical properties of quantumspin liquids. In particular, it allows for calculation ofthe temperature- and magnetic-field dependence of theirspecific heat, dynamic magnetic susceptibility χ and re-veals their scaling behavior [5, 6]. The theory relatessuch different phenomena as the QSL heat conductancein a magnetic field with the magnetoresistance in HFmetals, as well as with the spin relaxation rate in QSLand HF metals [9, 10]. Moreover, FC theory can describethe imaginary part of χ , exposing its scaling properties,which have been shown to be similar to those found inHF metals. The imaginary part of the dynamic suscep-tibility is of special importance since it can be directlymeasured in neutron scattering experiments [9]. Thus,the spin excitations in ZnCu (OH) Cl exhibit the samebehavior as electron excitations of the HF metal and,therefore form a continuum. Based on the good agree-ment with experiment achieved in the cited theoreticalstudies, the FC theory predicts the results of the key ex-periment of Han et al. [11] showing that the excitationsin the spin-liquid state of the kagome antiferromagnetform a dispersionless continuum [9].We were unable to check the results of the paper [1]because the presentation is fragmentary and lacks calcu-lated results for the observable physical properties of QSLaddressed above within FC theory. By contrast, withinthe context of FC theory, the presence of a flat band inherbertsmithite was predicted [5, 6] before its actual ex-perimental discovery [11]. All these results stand in vividcontrast with those of the paper [1], where only a quali-tative analysis of the dynamic structure factor S ( k , ω ) ispresented. Finally, as should already be apparent, refer-ences related to FC theory are absent from [1]. ∗ Electronic address: [email protected][1] Punk, M., Chowdhury, D. & Sachdev, S. Topological ex-citations and the dynamic structure factor of spin liquidson the kagome lattice.
Nat. Phys. , 289-293 (2014);arXiv:1308.2222.[2] Shaginyan, V.R., Amusia, M. Ya., Msezane, A.Z. &Popov, K.G. Phys. Reports
Scaling Behavior of HeavyFermion Metals. , 31-109 (2010).[3] Khodel, V.A. & Shaginyan, V.R. Superfluidity in systemswith fermion condensate.
JETP Lett. , 553 (1990).[4] Volovik G.E. A new class of normal Fermi liquids. JETP.Lett. , 222 (1991). [5] Shaginyan, V.R., Msezane, A.Z. & Popov, K.G. Ther-modynamic properties of the kagome lattice in herbert-smithite. Phys. Rev. B , 060401(R) (2011).[6] Shaginyan, V.R., Msezane, A.Z., Popov, K.G., Japaridze,G.S. & Stephanovich, V.A. Identification of strongly cor-related spin liquid in herbertsmithite. Europhys. Lett. ,56001 (2012).[7] Shaginyan, V.R., Msezane, A.Z., Popov, K.G., Clark,J.W., Zverev, M.V. & Khodel, V.A. Flat Bands andEnigma of Metamagnetic Quantum Critical Regime inSr Ru O . Phys. Lett. A , 2800 (2013).[8] Shaginyan, V.R., Msezane, A.Z., Popov, K.G., Japaridze,G.S. & Khodel, V.A. Common quantum phase transitionin quasicrystals and heavy-fermion metals.
Phys. Rev. B , 245122 (2013).[9] Shaginyan, V.R., Msezane, A.Z., Popov, K.G. & Khodel,V.A. Scaling in dynamic susceptibility of herbertsmithiteand heavy-fermion metals. Phys. Lett. A , 2622(2012).[10] Shaginyan, V.R., Msezane, A.Z., Popov, K.G., Japaridze,G.S. & Khodel, V.A. Heat transport in magneticfields by quantum spin liquid in the organic in-sulators EtMe Sb[Pd(dmit) ] and κ − (BEDT − TTF) Cu (CN) . Europhys. Lett. , 67006 (2013).[11] Han, T.-H., Helton, J. S., Chu, S., Nocera, D.N.,Rodriguez-Rivera, J.A., Broholm, C. & Lee, Y.S. Frac-tionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet.
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