| 1. |
- Eschmann, T., et al.
(författare)
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Thermodynamics of a gauge-frustrated Kitaev spin liquid
- 2019
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Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 1:3
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Tidskriftsartikel (refereegranskat)abstract
- Two- and three-dimensional Kitaev magnets are prototypical frustrated quantum spin systems, in which the original spin degrees of freedom fractionalize into Majorana fermions and a Z2 gauge field—a purely local phenomenon that reveals itself as a thermodynamic crossover at a temperature scale set by the strength of the bond-directional interactions. For conventional Kitaev magnets, the low-temperature thermodynamics reveals a second transition at which the Z2 gauge field orders and the system enters a spin-liquid ground state. Here, we discuss an explicit example that goes beyond this paradigmatic scenario—the Z2 gauge field is found to be subject to geometric frustration, the thermal ordering transition is suppressed, and an extensive residual entropy arises. Deep in the quantum regime, at temperatures of the order of one per mil of the interaction strength, the degeneracy in the gauge sector is lifted by a subtle interplay between the gauge field and the Majorana fermions, resulting in the formation of a Majorana metal. We discuss the thermodynamic signatures of this physics obtained from large-scale, sign-free quantum Monte Carlo simulations.
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| 2. |
- Eschmann, T., et al.
(författare)
-
Thermodynamics of a gauge-frustrated Kitaev spin liquid
- 2019
-
Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 1:3
-
Tidskriftsartikel (refereegranskat)abstract
- Two- and three-dimensional Kitaev magnets are prototypical frustrated quantum spin systems, in which the original spin degrees of freedom fractionalize into Majorana fermions and a Z2 gauge field - a purely local phenomenon that reveals itself as a thermodynamic crossover at a temperature scale set by the strength of the bond-directional interactions. For conventional Kitaev magnets, the low-temperature thermodynamics reveals a second transition at which the Z2 gauge field orders and the system enters a spin-liquid ground state. Here, we discuss an explicit example that goes beyond this paradigmatic scenario - the Z2 gauge field is found to be subject to geometric frustration, the thermal ordering transition is suppressed, and an extensive residual entropy arises. Deep in the quantum regime, at temperatures of the order of one per mil of the interaction strength, the degeneracy in the gauge sector is lifted by a subtle interplay between the gauge field and the Majorana fermions, resulting in the formation of a Majorana metal. We discuss the thermodynamic signatures of this physics obtained from large-scale, sign-free quantum Monte Carlo simulations.
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| 3. |
- Hermanns, Maria
(författare)
-
Conformal field theory construction for non-Abelian hierarchy wave functions
- 2017
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Ingår i: Physical Review B. - 2469-9950. ; 96:24
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Tidskriftsartikel (refereegranskat)abstract
- The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su(q)(k). For a subset of these states we are able to derive the conformal field theory description that makes the topological properties-in particular braiding-of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.
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| 4. |
- Kjäll, Jonas, et al.
(författare)
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Matrix product state representation of quasielectron wave functions
- 2018
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Ingår i: Journal of Statistical Mechanics-Theory and Experiment. - : IOP Publishing. - 1742-5468.
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Tidskriftsartikel (refereegranskat)abstract
- Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.
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| 5. |
- Matern, S., et al.
(författare)
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Entanglement in 3D Kitaev spin liquids
- 2018
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Ingår i: Journal of Statistical Mechanics-Theory and Experiment. - : IOP Publishing. - 1742-5468.
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Tidskriftsartikel (refereegranskat)abstract
- Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids axe the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures-ranging from topologically protected Weyl semimetals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Moreover, we find that in some cases the entanglement spectrum contains even more information about the topological features than the surface spectrum, and thus provides a simple and reliable tool to probe the topology of a system.
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| 6. |
- Revelli, A., et al.
(författare)
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Resonant inelastic x-ray incarnation of Young's double-slit experiment
- 2019
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Ingår i: Science Advances. - : American Association for the Advancement of Science (AAAS). - 2375-2548. ; 5:1
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 7. |
- Revelli, A., et al.
(författare)
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Spin-orbit entangled j=1/2 moments in Ba(2)CWeIrO(6) : A frustrated fcc quantum magnet
- 2019
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Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 100:8
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 8. |
- Revelli, A., et al.
(författare)
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Spin-orbit entangled j=1/2 moments in Ba2CeIrO6 : A frustrated fcc quantum magnet
- 2019
-
Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 100:8
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 9. |
- Tournois, Yoran, et al.
(författare)
-
Conformal field theory construction for non-Abelian hierarchy wave functions
- 2017
-
Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 96:24
-
Tidskriftsartikel (refereegranskat)abstract
- The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su(q)k. For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.
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| 10. |
- Wawrzik, D., et al.
(författare)
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Topological semimetals and insulators in three-dimensional honeycomb materials
- 2018
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Ingår i: Physical Review B. - 2469-9950. ; 98:11
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Tidskriftsartikel (refereegranskat)abstract
- Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter in graphene and other two-dimensional honeycomb materials. Here we introduce a family of three-dimensional honeycomb systems whose electronic band structures exhibit a variety of topological semimetals with Dirac nodal lines. We show that these nodal lines appear in varying numbers and mutual geometries, depending on the underlying lattice structure. They are stabilized, in most cases, by a combination of time-reversal and inversion symmetries and are accompanied by topologically protected "drumhead" surface states. In the bulk, these nodal line systems exhibit Landau level quantization and flat bands upon applying a magnetic field. In the presence of spin-orbit coupling, these topological semimetals are found to generically form (strong) topological insulators. This comprehensive classification of the electronic band structures of three-dimensional honeycomb systems might serve as guidance for future material synthesis.
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