| 1. |
- Bergholtz, E. J., et al.
(författare)
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Pfaffian quantum Hall state made simple : Multiple vacua and domain walls on a thin torus
- 2006
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 74:8, s. 081308-
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the Moore-Read Pfaffian state on a thin torus. The known sixfold degeneracy is realized by two inequivalent crystalline states with a four- and twofold degeneracy, respectively. The fundamental quasihole and quasiparticle excitations are domain walls between these vacua, and simple counting arguments give a Hilbert space of dimension 2n−1 for 2n−k holes and k particles at fixed positions and assign each a charge ±e∕4. This generalizes the known properties of the hole excitations in the Pfaffian state as deduced using conformal field theory techniques. Numerical calculations using a model Hamiltonian and a small number of particles support the presence of a stable phase with degenerate vacua and quarter-charged domain walls also away from the thin-torus limit. A spin-chain Hamiltonian encodes the degenerate vacua and the various domain walls.
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| 2. |
- Budich, Jan Carl, et al.
(författare)
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Topological insulators with arbitrarily tunable entanglement
- 2014
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 89:19, s. 195120-
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Tidskriftsartikel (refereegranskat)abstract
- We elucidate how Chern and topological insulators fulfill an area law for the entanglement entropy. By explicit construction of a family of lattice Hamiltonians, we are able to demonstrate that the area law contribution can be tuned to an arbitrarily small value but is topologically protected from vanishing exactly. We prove this by introducing novel methods to bound entanglement entropies from correlations using perturbation bounds, drawing intuition from ideas of quantum information theory. This rigorous approach is complemented by an intuitive understanding in terms of entanglement edge states. These insights have a number of important consequences: The area law has no universal component, no matter how small, and the entanglement scaling cannot be used as a faithful diagnostic of topological insulators. This holds for all Renyi entropies which uniquely determine the entanglement spectrum, which is hence also nonuniversal. The existence of arbitrarily weakly entangled topological insulators furthermore opens up possibilities of devising correlated topological phases in which the entanglement entropy is small and which are thereby numerically tractable, specifically in tensor network approaches.
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| 3. |
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| 4. |
- Hermanns, M., et al.
(författare)
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FQHE-the solvable limit and beyond
- 2008
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Ingår i: Bulletin of the American Physical Society.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We consider the quantum Hall system in the torus geometry. In the limit where the torus becomes thin, the problem is exactly solvable and the hierarchy of quantum Hall states is manifest. Explicit wave functions for a large set of them are constructed with help of conformal field theory. This construction provides a continuation from the exactly solvable limit to the experimental regime. Numerical results on 4/11 supports this picture.
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| 5. |
- Andersson, Birger, et al.
(författare)
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Towards a common ontology for business models
- 2006
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Ingår i: CEUR Workshop Proceedings.
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Konferensbidrag (refereegranskat)abstract
- To create an understanding of enterprises and the ways they do business, a starting point could be to identify the main actors and the values transferred between them. Business models are created in order to make clear who the business actors are in a business case and to make their relations explicit. The relations are formulated in terms of values exchanged between the actors. The purpose of the work reported in this paper is to create a better understanding of business models by identifying basic notions used in such models. It does so by constructing a common ontology based on three established business model ontologies: e3-value, REA, and BMO. By means of a careful analysis of these ontologies a conceptual schema is created that defines the common concepts. An example is worked out that explains how the common ontology should be understood.
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| 6. |
- Bergholtz, E.J., et al.
(författare)
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A simple view on the quantum Hall system
- 2007
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Ingår i: Bulletin of the American Physical Society.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The physics of the quantum Hall system becomes very simple on a thin torus. Remarkably, however, the rich structure of the system still exists in this limit. On the very thin torus the many body problem reduces to a one-dimensional classical electrostatic problem and both the abelian and the non-abelian quantum Hall states are manifested as gapped one-dimensional crystals, Tao-Thouless states, with fractionally charged excitations that appear as domain walls between degenerate ground states. These states represent, but are extreme forms of, the observed states in the bulk and their qualitative properties (such as quasiparticle degeneracies, quantum numbers, relative size of the gaps etc.) remain the same. For the gapless states, there is a phase transition at finite thickness to phases different from the gapped crystals. At half-filling in the lowest Landau level, this new phase is a Luttinger liquid of neutral dipoles which is adiabatically connected to the gapless state observed in the bulk. The existence of the gapless phase on the thin (but finite) torus provides an explicit microscopic example of how weakly interacting quasiparticles moving in a reduced (zero) magnetic field emerge as the low energy sector of strongly interacting electrons in a strong magnetic field.
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| 7. |
- Bergholtz, E.J., et al.
(författare)
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A simple view on the quantum Hall system
- 2008
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Ingår i: Quantum Magnetism. - 9781402085109 ; , s. 19-33
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Bokkapitel (refereegranskat)abstract
- The physics of the quantum Hall system becomes very simple when studied on a thin torus. Remarkably, however, the very rich structure still exists in this limit and there is a continuous route to the bulk system. Here we review recent progress in understanding various features of the quantum Hall system in terms of a simple one-dimensional model corresponding to the thin torus.
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| 8. |
- Bergholtz, E.J., et al.
(författare)
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An Exact Solution for the Half-filled Lowest Landau Level
- 2006
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Ingår i: Bulletin of the American Physical Society.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We present an exact solution for the interacting electron gas in the half-filled lowest Landau level on a thin torus. The low energy sector consists of non-interacting, one-dimensional, neutral fermions (dipoles). The ground state, which is homogeneous, is the Fermi sea obtained by filling the negative energy states and the excited states are the gapless neutral excitations out of this one-dimensional sea. We identify this ground state as a version of the Rezayi-Read state, and find that it develops continuously, as the circumference grows, into the Rezayi-Read state that is believed to describe the observed metallic phase in the two-dimensional system. This suggests a Luttinger liquid description of the half-filled Landau level.
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