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  • 1.
    Bergholtz, Emil Johansson
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Hansson, Hans
    Stockholm University, Faculty of Science, Department of Physics.
    Hermanns, Maria
    Stockholm University, Faculty of Science, Department of Physics.
    Karlhede, Anders
    Stockholm University, Faculty of Science, Department of Physics.
    Microscopic theory of the quantum Hall hierarchy2007In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 99, no 25, p. 256803-1-256803-4Article in journal (Refereed)
    Abstract [en]

    We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan et al., and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.

  • 2.
    Bergholtz, Emil Johansson
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Hansson, Thors Hans
    Stockholm University, Faculty of Science, Department of Physics.
    Hermanns, Maria
    Stockholm University, Faculty of Science, Department of Physics.
    Karlhede, Anders
    Stockholm University, Faculty of Science, Department of Physics.
    Viefers, Susanne
    Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states2008In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 77, no 16, p. 165325-1-165325-9Article in journal (Refereed)
    Abstract [en]

    Laughlin’s wave functions, which describe the fractional quantum Hall effect at filling factorsν=1/(2k+1), can be obtained as correlation functions in a conformal field theory, and recently, this construction was extended to Jain’s composite fermion wave functions at filling factors ν=n/(2kn+1). Here, we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, which are the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multihole states, make the connection to Wen’s general classification of Abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally, we discuss to what extent our wave functions can be described in the language of composite fermions.

  • 3.
    Hansson, Thors Hans
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Hermanns, Maria
    Stockholm University, Faculty of Science, Department of Physics.
    Viefers, Susanne
    Regnault, N
    Conformal Field Theory Approach to Abelian and Non-Abelian Quantum Hall Quasielectrons2009In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 102, no 16, p. 166805-1-166805-4Article in journal (Refereed)
    Abstract [en]

    The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.

  • 4.
    Hermanns, Maria
    Stockholm University, Faculty of Science, Department of Physics.
    Condensing Non-Abelian Quasiparticles2010In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 104, no 5, p. 056803-1-056803-4Article in journal (Refereed)
    Abstract [en]

    A most interesting feature of certain fractional quantum Hall states is that their quasiparticles obey non-Abelian fractional statistics. So far, candidate non-Abelian wave functions have been constructed from conformal blocks in cleverly chosen conformal field theories. In this work we present a hierarchy scheme by which we can construct daughter states by condensing non-Abelian quasiparticles (as opposed to quasiholes) in a parent state, and show that the daughters have a non-Abelian statistics that differs from the parent. In particular, we discuss the daughter of the bosonic, spin-polarized Moore-Read state at ν=4/3 as an explicit example.

  • 5.
    Hermanns, Maria
    Stockholm University, Faculty of Science, Department of Physics.
    Quasielectrons in Abelian and non-Abelian Quantum Hall States2010Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Strongly correlated electron systems continue to  attract a lot of interest. Especially two-dimensional electron systems have shown many surprising behaviours. A fascinating example is the quantum Hall effect, which arises when electrons are confined to two dimensions, subjected to a very large magnetic field, and cooled to very low temperatures. Under these conditions, the electrons form new states of matter - the strongly correlated quantum Hall liquids. A hallmark of these quantum liquids is the precise quantization of the Hall conductance, but in recent years more attention has been focused on their exotic excitations. These have fractional electric charge, and fractional exchange statistics. The latter implies that the wave function is multiplied by a phase factor containing a fractional phase when two quasiparticles are moved around each other. Thus, they are neither bosons nor fermions, but so-called anyons. In recent years, there has accumulated theoretical and experimental evidence  for some of the quantum Hall liquids having even more exotic excitations with not only fractional but non-Abelian exchange statistics. The quasiparticles of such systems could be used to build topologically protected quantum bits, which are much more robust than presently available quantum bits; they would be the ideal building blocks of a quantum computer.

     We use conformal field theory to describe the quantum Hall liquids, as well as their excitations. In particular, we represent the electrons and quasiparticles by conformal field theory operators. Even though the operator description for quasiholes is very well understood, it was for a long time unclear how to describe their antiparticles, the quasielectrons. We found an operator  that describes quasielectron excitations correctly and shares many of the useful properties of the corresponding quasihole operator. For instance, many of the topological properties of the particles are manifest in the operator. This not only adds a missing piece to the quantum Hall puzzle,  but it also opens up new and exciting possibilities. For instance, we were able to extend this construction to the non-Abelian states. A highly non-trivial application of our approach is the condensation of non-Abelian quasielectrons, which yields new non-Abelian quantum Hall states with non-Abelian properties that differ from those of their parent states.

  • 6.
    Hermanns, Maria
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Suorsa, Juha
    Bergholtz, Emil Johansson
    Stockholm University, Faculty of Science, Department of Physics.
    Hansson, Thors Hans
    Karlhede, Anders
    Stockholm University, Faculty of Science, Department of Physics.
    Quantum Hall wave functions on the torus2008In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 77, no 12, p. 125321-1-125321-16Article in journal (Refereed)
    Abstract [en]

    We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at, e.g., ν=4∕11. The techniques we use constitute a nontrivial extension of the conformal field theory methods developed earlier to construct the corresponding wave functions in disk geometry.

  • 7. Mishchenko, Petr A.
    et al.
    Kato, Yasuyuki
    O'Brien, Kevin
    Bojesen, Troels A.
    Eschmann, Tim
    Hermanns, Maria
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Trebst, Simon
    Motome, Yukitoshi
    Chiral spin liquids with crystalline Z(2) gauge order in a three-dimensional Kitaev model2020In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 101, no 4, article id 045118Article in journal (Refereed)
    Abstract [en]

    Chiral spin liquids (CSLs) are time-reversal-symmetry-breaking ground states of frustrated quantum magnets that show no long-range magnetic ordering but instead exhibit topological order and fractional excitations. Their realization in simple and tractable microscopic models has, however, remained an open challenge for almost two decades until it was realized that Kitaev models on lattices with odd-length loops are natural hosts for such states, even in the absence of a time-reversal-symmetry-breaking magnetic field. Here we report on the formation of CSLs in a three-dimensional Kitaev model on a hypernonagon lattice composed of nine-site loops, which differ from their widely studied two-dimensional counterparts; namely, they exhibit a crystalline ordering of the Z(2) gauge fluxes and thereby break some of the underlying lattice symmetries. We study the formation of these unconventional CSLs via extensive quantum Monte Carlo simulations and demonstrate that they are separated from the featureless paramagnet at high temperatures by a single first-order phase transition at which both time-reversal and lattice symmetries are simultaneously broken. Using variational approaches for the ground state, we explore the effect of varying the Kitaev couplings and find at least five distinct CSL phases, all of which possess crystalline ordering of the Z(2) gauge fluxes. For some of these phases, the complementary itinerant Majorana fermions exhibit gapless band structures with topological features such as Weyl nodes or nodal lines in the bulk and Fermi arc or drumhead surface states.

  • 8. Revelli, A.
    et al.
    Loo, C. C.
    Kiese, D.
    Becker, P.
    Fröhlich, T.
    Lorenz, T.
    Sala, M. Moretti
    Monaco, G.
    Buessen, F. L.
    Attig, J.
    Hermanns, Maria
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Streltsov, S.
    Khomskii, D.
    van den Brink, I. J.
    Braden, M.
    van Loosdrecht, P. H. M.
    Trebst, S.
    Paramekanti, A.
    Grüninger, M.
    Spin-orbit entangled j=1/2 moments in Ba(2)CWeIrO(6): A frustrated fcc quantum magnet2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 100, no 8, article id 085139Article in journal (Refereed)
    Abstract [en]

    We establish the double perovskite Ba2CeIrO6 as a nearly ideal model system for j = 1/2 moments, with resonant inelastic x-ray scattering indicating that the ideal j = 1/2 state contributes by more than 99% to the ground-state wave function. The local j = 1/2 moments form an fcc lattice and are found to order antiferromagnetically at T-N = 14 K, more than an order of magnitude below the Curie-Weiss temperature. Model calculations show that the geometric frustration of the fcc Heisenberg antiferromagnet is further enhanced by a next-nearest neighbor exchange, and a significant size of the latter is indicated by ab initio theory. Our theoretical analysis shows that magnetic order is driven by a bond-directional Kitaev exchange and by local distortions via a strong magnetoelastic effect. Both, the suppression of frustration by Kitaev exchange and the strong magnetoelastic effect are typically not expected for j = 1/2 compounds making Ba2CeIrO6 a riveting example for the rich physics of spin-orbit entangled Mott insulators.

  • 9. Revelli, A.
    et al.
    Sala, M. Moretti
    Monaco, G.
    Becker, P.
    Bohaty, L.
    Hermanns, Maria
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Universität zu Köln, Germany; University of Gothenburg, Sweden.
    Koethe, T. C.
    Fröhlich, T.
    Warzanowski, P.
    Lorenz, T.
    Streltsov, S. V.
    van Loosdrecht, P. H. M.
    Khomskii, D. I.
    van den Brink, J.
    Grüninger, M.
    Resonant inelastic x-ray incarnation of Young's double-slit experiment2019In: Science Advances, E-ISSN 2375-2548, Vol. 5, no 1, article id eaav4020Article in journal (Refereed)
    Abstract [en]

    Young's archetypal double-slit experiment forms the basis for modern diffraction techniques: The elastic scattering of waves yields an interference pattern that captures the real-space structure. Here, we report on an inelastic incarnation of Young's experiment and demonstrate that resonant inelastic x-ray scattering (RIXS) measures interference patterns, which reveal the symmetry and character of electronic excited states in the same way as elastic scattering does for the ground state. A prototypical example is provided by the quasi-molecular electronic structure of insulating Ba3CeIr2O9 with structural Ir dimers and strong spin-orbit coupling. The double slits in this resonant experiment are the highly localized core levels of the two Ir atoms within a dimer. The clear double-slit-type sinusoidal interference patterns that we observe allow us to characterize the electronic excitations, demonstrating the power of RIXS interferometry to unravel the electronic structure of solids containing, e.g., dimers, trimers, ladders, or other superstructures.

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